TREASURY  DEPARTMENT 
U.  S.  COAST  AND  GEODETIC  SURVEY 

W.  W.  DUFFIELD 

SUPERINTENDENT 


TOPOGRAPHY 


PHOTO -TOPOGRAPHIC  METHODS  AND  INSTRUMENTS 


By  J".  A..  FLEMER,  Assistant 


APPENDIX  No.  10— REPORT  FOR  1897 


- 


GOVERNMENT  PRINTING  OFFICE 
1898 


Hs  \\<\% 

TREASURY  DEPARTMENT 

CT.  S.  COAST  AND  GEODETIC  SURVEY 

W.  W.  DUFFIELD 

SUPERINTENDENT 


TOPOGRAPHY 


PHOTO -TOPOGRAPHIC  METHODS  AND  INSTRUMENTS 


By  .T.  A..  BBBTVTIKR,  Assistant 


APPENDIX  No.  10— REPORT  FOR  1897 


WASHINGTON 

GOVERNMENT  PRINTING  OFFICE 
1898 


APPENDIX  NO.  10—1897. 


PHOTOTOPOGRAPH  1C  METHODS  AND  INSTRUMENTS. 


By  ,T.  A.  FLEMER,  Assistant. 


619 


Digitized  by  the  Internet  Archive 
in  2016 


https://archive.org/details/phototopographicOOflem 


[PHOTOTOPOGRAPHIC  METHODS  AND  INSTRUMENTS.] 


CONTENTS. 


Page. 

Preface 625 

Introduction 627 

Chapter  I. 

FUNDAMENTAL  PRINCIPLES  OF  ICONOMETRY. 

I.  Orienting  the  picture  traces  on  the  working  sheet 631 

1.  Using  a surveying  camera - 631 

2.  Using  a camera  or  phototheodolite 632 

II.  Arithmetical  determination  of  the  principal  and  horizon  lines 633 

1.  Determination  of  the  principal  point  and  of  the  distance  line  of  the  perspective 633 

2.  Determination  of  the  position  of  the  horizon  line  on  the  perspective 634 

III.  Graphic  method  for  determining  the  positions  of  the  principal  and  horizon  lines  on  the  perspective 635 

IV.  The  five-point  problem  (by  Prof.  F.  Steiner).  Locating  the  position  of  the  camera  station  by  means  of 

the  perspective  when  five  triangulation  points  are  pictured  on  one  photograph 636 

1.  Determination  of  the  principal  point  and  of  the  distance  line . 637 

2.  Simplified  construction  for  locating  the  camera  station  by  means  of  the  five-poiut  problem.. 637 

3.  Application  of  the  five-point  problem  for  the  special  case  when  the  five  points  are  ranged  into  a 

triangle 638 

4.  To  find  the  elevation  of  a camera  station  that  had  been  located  by  means  of  the  five-point  problem.  638 

V.  The  three-point  problem . 639 

1.  Using  the  three-arm  protractor;  mechanical  solution  of  the  thx-ee-point  problem  640 

2.  Graphic  solution  of  the  three-point  problem 640 

(а)  Using  the  so-called  two-circle  method 640 

(б)  Using  the  method  of  Bohnenberger  and  Bessel 640 

VI.  Orientation  of  the  picture  traces,  based  upon  instrumental  measurements  made  in  the  field 641 

VII.  Relations  between  two  perspectives  of  the  same  object  viewed  from  different  stations;  Prof.  G.  Hauek’s 

method 641 

1.  “ Kernelpoints”  and  “kernelplanes” 641 

2.  Use  of  the  line  of  intersection  of  two  picture  planes  showing  identical  objects  viewed  from  two 

different  stations 643 

VIII.  To  plat  a figure,  situated  in  a horizontal  plane,  on  the  ground  plan  by  means  of  its  perspective 645 

IX.  To  draw  a plane  figure  on  the  ground  plan  by  means  of  the  “method  of  squares”  if  its  perspective  and 

the  elements  of  the  vertical  picture  plane  are  given 649 

X.  The  use  of  the  “vanishing  scale” ..  651 

Chapter  II. 

PHOTOGRAPHS  ON  INCLINED  PLANES. 

I.  To  plat  the  picture  trace  of  an  inclined  plate 654 

II.  To  plat  the  lines  of  direction  to  points  pictured  on  an  inclined  photographic  plate 656 

III.  Determination  of  the  altitudes  of  points  pictured  on  inclined  photographic  plates 656 

IV.  Application  of  Professor  Hauck’s  method 657 

Chapter  III. 

PHOTOTOPOGRAPHIC  METHODS. 

I.  Analytical  or  arithmetical  iconometric  methods 659 

1.  Method  of  Prof.  \V.  Jordan 659 

2.  Method  of  Dr.  G.  Le  Bon 660 


621 


622 


CONTENTS. 


Chapter  III — Continued. 
phototopograhic  METHODS — continued. 

I.  Analytical  or  arithmetical  iconometric  methods — Continued.  Page. 

3.  Method  of  L.  P.  Paganini  (Italian  method) 661 

General  determination  of  the  elements  of  the  Italian  photographic  perspectives 662 

(а)  Orientation  of  the  picture  trace 662 

(б)  Platting  of  the  lines  of  direction  to  pictured  points  of  the  terrene 662 

(c)  Determination  of  the  elevations  of  pictured  points 663 

(d)  Checking  the  position  of  the  horizon  line  on  a photograph 664 

(e)  Determination  of  the  focal  length 665 

(/)  Determination  of  the  principal  point  of  the  perspective 665 

( g )  Application  of  Franz  Hafferl’s  method  for  finding  the  focal  length  of  a photographic  per- 
spective from  the  absciss®  of  two  pictured  known  points 668 

4.  General  arithmetical  method  for  finding  the  platted  positions  of  points  pictured  on  vertically 

exposed  photographic  plates  (negatives) 668 

5.  General  arithmetical  method  for  finding  the  platted  positions  of  points  pictured  on  inclined  photo- 

graphic plates 671 

6.  General  arithmetical  determination  of  the  elements  of  photographic  perspectives 672 

II.  Graphical  iconometric  methods 674 

1.  Method  of  Col.  A.  Laussedat 674 

(а)  Locating  points,  identified  on  several  photographs,  on  the  platting  sheet 676 

(б)  Determination  of  the  elevations  of  pictured  points 676 

(c)  Drawing  the  plan,  including  horizontal  contours 677 

2.  Method  of  Dr.  A.  Meydenbaur 677 

(а)  Determination  of  the  focal  length  for  the  panorama  views 678 

(б)  General  method  of  iconometric  platting 678 

(c)  Determination  of  the  elevations  of  pictured  points  of  the  terrene 681 

3.  Method  of  Capt.  E.  Devillo  (Canadian  method) 681 

(а)  General  remarks  on  the  field  work 681 

(б)  General  remarks  on  the  iconometric  platting  of  the  survey 683 

(c)  Platting  the  picture  traces 684 

(d)  The  identification  of  points,  pictured  on  several  photographs,  representing  the  same  points  of 

the  terrene 685 

(e)  Application  of  Professor  Hauck’s  method  for  the  identification  of  points  on  two  photographs.  685 

(/)  Platting  the  intersections  of  horizontal  directions  to  pictured  points 686 

(g)  Platting  pictured  points  icouometrically  by  “vertical  intersections” 687 

( h ) Iconometric  determination  of  elevations 689 

(i)  Iconometric  determination  of  elevations  by  means  of  the  “scale  of  heights” 690 

(j)  The  use  of  the  so-called  “photograph  board” 691 

(fc)  Constructing  the  traces  of  a figure’s  plane 692 

(l)  Contouring 694 

( m ) The  photograph  protractor 696 

4.  Method  of  V.  Legros  for  determining  the  position  of  the  horizon  line 697 

5.  Method  of  Prof.  S.  Finsterwalder  for  the  iconometric  location  of  horizontal  contours^ 697 


Chapter  IV. 


I'll  OTOGR  AM  METE  US. 

I.  Requirements  to  be  fulfilled  by  a topographic  surveying  camera 699 

II.  Ordinary  cameras  (with  bellows)  made  adapted  for  surveying 699 

III.  Special  surveying  cameras  with  constant  focal  lengths 701 

1.  Dr.  A.  Meydenbaur’s  surveying  camera 701 

2.  E.  Devillo’s  new  surveying  camera 701 

3.  Use  of  the  instruments  comprised  in  the  Canadian  phototopographic  outfit 705 

4.  United  States  Coast  and  Geodetic  Survey  camera 706 

I V.  Surveying  cameras  combined  with  geodetic  instruments  (phototheodolites,  photographic  plane  tables,  etc.) . 706 

1.  The  new  Italian  phototheodolite,  devised  by  L.  P.  Paganini 708 

2.  The  photogramme  trie  theodolite  of  Prof.  S.  Finsterwalder r 711 

3.  Phototheodolite  for  precise  work,  by  O.  Ney 712 

4.  The  phototheodolite  of  Dr.  C.  Ivoppe 715 

5.  Phototheodolite  devised  by  V.  Pollack 716 

6.  Col.  A.  Laussedat’s  new  phototheodolite - 717 

7.  The  phototheodolite  of  Starke  and  Kammerer 717 

8.  Captain  Hiibl’s  plane  table  photogrammeter 721 

V.  Panoramic  cameras 722 

The  topographic  cylindrograph  of  R.  Moessard 722 


CONTENTS. 


623 


Chapter  V. 

ICONOMETERS  AND  PEKSPECTOGRAPHS. 

Page. 

I.  The  graphic  protractor 725 

II.  The  graphic  sector  (“settore  grafico”) 725 

III.  The  graphic  hypsometer 725 

IV.  The  centrolinead 725 

1.  To  set  the  arms  of  the  centrolinead,  if  the  direction  to  the  vanishing  point  is  given,  by  a line  in  the 

ground  plan 727 

2.  To  set  the  arms  of  the  centrolinead  if  the  given  line  belongs  to  the  perspective 727 

V.  The  perspectometer 728 

The  use  of  the  perspectometer 728 

VI.  The  perspectograpli  (H.  Ritter’s  instrument) 729 

The  use  of  the  perspectograpli 731 

VII.  Professor  Hauck’s  trikolograpli 732 


PREFACE. 


In  the  annual  report  of  the  Superintendent  of  the  United  States  Coast  and  Geodetic  Survey 
for  1893,  Appendix  No.  3,  a description  is  given  of  phototopography  as  practiced  in  Italy  and  in 
the  Dominion  of  Canada. 

The  Canadian  surveying  camera  and  the  Italian  phototheodolite,  which  have  been  described 
in  said  appendix  (No.  3,  1893),  have  both  been  replaced  by  improved  and  more  effective  instru- 
ments, which  will  be  described  in  the  paper  herewith  presented,  together  with  other  photographic 
surveying  instruments  that  may  be  regarded  as  typical  representations  of  the  different  forms 
now  in  use. 

Notwithstanding  the  rapid  rise  in  the  popularity  of  photographic  surveying  in  general,  we 
still  meet  with  many  who  express  doubt  as  to  the  practical  value  and  accuracy  of  photographic 
surveying  methods,  either  from  ignorance  of  those  methods,  from  defective  results  obtained  from 
the  application  of  photography  to  the  survey  of  areas  not  adapted  for  a phototopograpliic  devel- 
opment, or,  more  frequently,  from  that  extreme  conservatism  which  meets  all  innovations  with 
more  or  less  doubt  and  distrust.  Others,  again,  may  have  failed  to  take  kindly  to  photographic 
surveying,  supposing  a thorough  familiarity  with  the  theories  and  laws  of  optics,  descriptive 
geometry,  perspective  drawing,  and  general  cartography  to  be  essentials,  without  which  no  prac- 
tical knowledge  and  understanding  of  pliotogrammetry  may  be  obtained. 

Although  it  should  be  admitted  that  such  knowledge  will  enable  the  student  to  master  photo- 
topography  in  a rapid  and  easy  manner,  giving  him  a great  advantage  in  and  an  enlarged  field 
for  the  practical  application  of  the  same,  or  in  teaching  its  methods  to  others,  yet  the  fundamental 
principles  underlying  this  art  are  so  simple  that  it  is  believed  any  topographer  or  land  surveyor, 
with  the  knowledge  that  he  should  possess  as  such,  can  readily  acquire  enough  of  the  theoretical 
fundamental  principles  to  become  fully  able  to  apply  photography  successfully  to  practical  surveys. 

Although  it  will  not  fall  within  the  scope  of  this  paper  to  enter  into  the  study  of  either  optics, 
descriptive  geometry,  perspective,  photo-chemical  analysis,  or  cartography,  it  will  show  in  a gen- 
eral manner  how  photography  has  been  applied  to  topographic  surveys  by  describing  the  simple 
processes  and  methods  that  will  suffice  to  direct  beginners  in  their  practical  applications,  leaving 
it  to  experience  and  subsequent  special  study  to  determine  the  measure  of  success,  the  more  so  as 
several  .excellent  works  and  text-books  on  photographic  surveying  have  recently  been  published 
in  the  English,  French,  Italian,  and  German  languages. 

The  compiler  of  this  paper  having  consulted  all  available  publications  describing  photo- 
topographic  methods,  both  foreign  and  domestic,  gladly  expresses  his  indebtedness  for  information 
on  this  subject  to  Capt.  E.  Deville,  survey  or- general  of  Dominion  lands;  to  Mr.  W.  F.  King, 
Alaskan  boundary  commissioner  to  Her  Majesty,  Ottawa,  Canada;  to  Col.  A.  Laussedat,  director 
of  the  Conservatoire  des  Arts  et  Metiers,  Paris;  and  particularly  to  the  following  publications : 

La  Fototopografia  in  Italia,  Eivista  Marittima,  L.  P.  Paganini,  1889,  Fasc.  YI  and  YII. 

Nuovi  Appunti  di  Fototopografia,  Eivista  Marittima,  L.  P.  Paganini,  1894,  E.  C.  Forzani. 

Zeitschrift  fur  Vermessungswesen. 

Die  pliotographische  Messkunst,  Prof.  Franz  Schiffner,  Halle  a.  S.,  Wilhelm  Knapp,  1892. 

Photographic  Surveying,  E.  Deville,  Ottawa,  1895. 

Zeitschrift  fiir  Instrumentenkunde. 

Comptes  Eendus  de  l’Academie  des  Sciences,  Paris,  Eevue  Scientifique,  No.  20,  I;  No.  3,  II; 
1894. 

Die  photograph ische  Messkunst,  Franz  Schiffner,  Halle  a.  S.,  1892. 

6584 40 


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APPENDIX  NO.  10—1897. 


PHOTOTOPOGrRAPHIC  METHODS  AND  INSTRUMENTS. 


By  J.  A.  Flemer. 


INTRODUCTION. 

Topography  is  that  branch  of  surveying  which  pictures  the  shape  of  the  outer  visible  surface 
of  the  earth,  in  reduced  scale,  as  a horizontal  projection,  yet  showing  the  relative  positions  of 
points  of  the  terrene  also  in  the  vertical  sense.  It  is,  therefore,  supplementary  to  geodesy  in 
representing  areas  of  the  earth’s  surface,  including  all  the  necessary  details  and  changes  in  the 
terrene,  by  means  of  instrumental  measurements  made  in  the  field. 

The  work  of  filling  in  the  details — topographic  surveying  in  the  closer  sense — may  be 
accomplished  by  various  methods,  differing  in  the  matter  of  costs,  time,  and  attainable  accuracy; 
one  may  be  advantageously  employed  for  one  class  of  work,  while  another  may  be  preferable  for 
another  class  or  locality,  under  different  conditions,  and  the  method  best  adapted  for  any  partic- 
ular region  should  be  employed  to  obtain  the  best  results.  Minute  and  detailed  methods,  with 
ensuing  accurate  results,  should  be  applied  to  cities  and  all  closely  settled  regions,  to  the  coastal 
belts,  larger  river  valleys  and  lakes,  particularly  when  navigable,  and  this  work  should  be  platted 
on  a large  scale. 

Arid,  barren,  and  mountainous  regions,  as  well  as  prairies  and  swamp  lands,  when  sparsely 
settled,  should  be  more  generalized  in  their  cartographic  representation  and  platted  on  a small 
scale. 

Topographic  surveys  may  be  accomplished  in  various  ways,  of  which  the  following  are  the 
methods  and  instrumental  outfits  more  frequently  in  use: 

I.  The  direct  platting  to  scale  in  the  field  of  all  features  to  be  represented  on  the  finished 
chart : 

(a)  With  a plane-table  and  steel  tape  measure. 

(b)  With  a plane-table  and  telemeter  or  stadia  rods. 

(c)  With  a tachygraphometer  and  telemeter  or  stadia  rods. 

(d)  With  either  outfit  mentioned  under  a.  and  h , but  with  a leveling  instrument  in  addition  for 
a more  precise  location  of  the  horizontal  contours. 

(e)  Using  a barometer  instead  of  a level  for  less  accurate  work. 

II.  The  compilation  of  all  available  data — cadastral  surveys,  public  land  and  county  surveys, 
railroad  and  canal  surveys — giving  principally  the  horizontal  distances  and  making  a supple- 
mentary survey  to  supply  the  missing*  data,  which  in  this  case  are  principally  elevations  that  may 
be  supplied  by  leveling  profiles,  by  trigonometric  leveling,  by  interpolation  and  sketching. 

III.  The  records  of  the  survey  are  in  the  shape  of  field  notes  and  sketches  (tachymetry),  the 
map  being  produced  by  platting  the  recorded  data  in  the  office: 

(a)  With  a surveyor’s  compass  and  steel  tape,  locating  the  relative  positions  of  characteristic 
points  in  the  horizontal  sense,  while  their  relative  elevations  are  ascertained  by  means  of  a level 
and  minor  details  are  sketched. 

( b ) By  means  of  a transit  and  steel  tape  points  are  determined  both  geographically  and 
hypsometrically  (using  vertical  angles),  and  minor  details  by  sketching. 


628 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


(c)  By  means  of  a transit  and  telemeter  or  stadia  rods. 

( d ) By  means  of  a tachymeter  and  stadia  rods  (elevations  being  obtained  mechanically  with 
the  instrument). 

(e)  By  means  of  a transit  with  steel  tape  or  telemeters,  combined  with  a leveling  instrument 
(fcr  locating  horizontal  contours). 

(/)  By  using  a specially  constructed  aneroid  barometer  ^Goldschmidt’s)  in  place  of  the  level 
for  locating  and  tracing  the  horizontal  contours  in  the  field. 

IY.  The  field  records  for  developing  the  terrene  are  represented  by  photographic  negatives, 
taken  under  special  conditions  (for  phototopograpliic  purposes)  from  known  stations: 

(а)  With  a camera  or  phototheodolite,  telemeters,  or  other  distance  measures  (and  often  a 
barometer  for  obtaining  elevations). 

(б)  With  a surveying  camera,  a separate  theodolite,  telemeters  and  aneroid  barometer. 

(c)  With  a photographic  plane  table,  a distance  measure,  and  aneroid  barometer. 

(d)  With  a surveying  camera,  a separate  plane  table,  and  distance  measure,  frequently  using 
an  aneroid  barometer  for  camera  stations  occupied  without  the  plane  table. 

Y.  The  topographic  survey  may  be  accomplished  by  means  of  a specially  constructed  survey- 
ing camera  attached  to  a free  or  captive  balloon. 

After  the  area  which  is  to  be  surveyed  has  been  covered  with  a net  of  triangles  and  polygons 
it  will  have  been  provided  with  a framework  of  lines  of  known  lengths  and  direction  (triangulation), 
forming  a skeleton  survey  of  the  country,  and  after  the  natural  and  artificial  features  have  been 
filled  in  by  one  of  the  numerous  topographic  methods  (just  mentioned)  with  more  or  less  detail 
and  accuracy  we  will  have  a topographic  survey  of  the  area  of  more  or  less  precision. 

A good  example  of  changing  the  method  with  the  locality  may  be  cited  in  the  new  survey  of 
Italy,  wliere  Paganini’s  results  fully  proved  the  efficiency  of  phototopography  for  alpine  work 
(platted  on  a scale  of  1 : 25000  and  1 : 50000)  and  led  to  the  adoption  of  the  phototheodolite  as  an 
auxiliary  instrument  to  the  plane  table,  the  latter  being  used  for  mapping  the  areas  below  2,000 
meters,  while  the  phototheodolite  was  exclusively  used  for  the  delineation  of  the  terrene  situated 
above  that  altitude. 

Pliotogrammetry  proper  (or  me  trap  h o t o graph  y ) should  be  applied  to  the  art  of  taking  perspec- 
tive views  of  buildings  with  a photographic  camera  for  the  purpose  of  constructing  therefrom  their 
elevations  and  ground  plans,  and  it  is  used  principally  for  architectural,  archaeological,  and  engi- 
neering purposes. 

The  term  phototopography  (or  topophotography)  should  be  generally  adopted  for  all  topographic 
surveys  based  on  perspective  views  of  the  terrene  obtained  by  means  of  the  camera. 

Under  photographic  survey  we  could  then  class  all  surveys  based  on  photographic  data  which 
do  not  include  the  orographic  delineation  of  the  terrene. 

Iconometry  means  the  measuring  of  dimensions  of  objects  from  their  perspectives  (“Bildmess- 
kunst”),  and  this  term  could  well  be  applied  to  those  graphic  constructions  which  serve  to  convert 
perspectives  into  horizontal  projections;  iconometry  is  the  reverse  of  perspective  drawing. 

Photography  has  been  very  successfully  employed  for  topographic  surveys  in  Italy,  Austria, 
and  Canada,  and  for  the  production  of  the  extensive  topographic  reconnaissance  maps  of  south- 
eastern Alaska. 

Although  this  method,  invented  and  elaborated  by  Colonel  Laussedat,  found  its  first  appli- 
cation in  France,  still,  both  in  France  and  in  Germany,  it  was  originally  preempted  by  the  mili- 
tary authorities,  under  whose  auspices  it  was  developed  and  chiefly  used  for  so-called  secret  or 
military  surveys;  lately,  however,  photography  has  found  a wider  and  more  general  application 
to  surveying  in  those  two  countries,  and  we  find  this  method  now  in  use  also  in  Greece,  Spain, 
Portugal,  Norway,  Belgiuni,  Mexico,  Chile,  Peru,  Tonquin,  Brazil,  Argentine  Republic,  Switzer- 
land, and  England. 

Although  Lieut.  Henry  A.  Reed  has,  for  several  years  past,  taught  phototopography,  theoret- 
ically and  practically,  at  the  United  States  Military  Academy  at  West  Point,  there  seems  to  be  no 
record  of  any  further  work  of  this  kind  undertaken  by  others  in  the  United  States. 

In  the  following  paper  we  will  treat  principally  of  those  photogram  metric  methods  which  are 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


629 


applicable  to  topographic  surveys,  although  the  same  principles  underlie  also  the  methods  in  use 
when  applying  photography  to — 

Geological  surveys. — For  the  study  of  changes  in  glaciers  (glacial  motion  or  variation)  based 
upon  the  comparison  of  glacier  maps,  obtained  at  stated  time  intervals  from  identical  and  known 
camera  stations ; for  volcanic  eruptions  and  their  effects;  for  the  study  of  periodical  changes  in 
sand  dunes  due  to  recurrent  winds  blowing  from  one  direction  at  regular  intervals,  etc. 

Meteorologic  observations. — For  the  study  of  the  higher  aerial  currents  and  cloud  altitudes, 
based  upon  iconometric  cloud  charts,  obtained  by  simultaneous  photographic  records  on  plates 
exposed  at  different  stations  at  stated  time  intervals;  for  the  study  of  the  paths  of  lightning, 
their  lengths,  etc. 

Hydrographic  surveys. — For  the  location  of  rocks,  buoys,  etc. ; for  the  study  of  fluvial  currents, 
riparian  changes  due  to  corrosion,  erosion,  etc.;  for  obtaining  coast  views  from  points  marked  on 
the  sailing  charts  to  facilitate  the  locating  of  the  position  of  vessels  when  approaching  laud,  etc. 

Engineering . — To  estimate  the  amount  of  work  done  at  any  date  by  means  of  photographic 
surveys  that  show  the  status  of  the  work  (excavations,  fills,  structural  buildings,  etc.)  at  stated 
time  intervals,  etc. 

Architectural  purposes. — For  constructing  the  ground  plans  and  elevations  of  old  buildings 
from  their  perspective  views  (photographs),  for  purposes  of  remodeling,  renovation,  or  preservation. 

Military  and  secret  surveys,  and  so  on. 


CHAPTER  I. 


FUNDAMENTAL  PRINCIPLES  OF  ICONOMETRY. 

If  only  one  perspective  of  an  object,  including  its  distance  line,  the  principal  point,  and  the 
horizon  line  is  given — in  other  words,  if  the  point  of  view  and  the  central  projection  upon  a 
vertical  plane  of  an  object  are  given — the  object  itself  can  not  yet  be  determined  regarding  its 
position  and  dimensions.  In  the  same  way  the  geographic  position  of  a point  can  not  be  located 


by  means  of  the  plane  table  from  a known  station,  unless  direct  measurements  to  ascertain  the 
distance  of  such  point  from  the  station  are  resorted  to. 

If,  however,  two  different  perspectives  (including  their  elements)  of  the  same  object,  obtained 
from  two  different  known  stations,  are  given,  the  dimensions  and  the  position  of  the  object  with 
reference  to  the  two  stations  may  be  determined  iconometrically  in  a manner  analogous  to  that  in 


\ 


\ 

I 

i 

/ 

/ 

/ 

/ 

/ 

/ 


which  a point  is  located  (by  intersection)  on  the  plane-table  sheet  by  being  observed  upon  from 
two  different  plane  table  stations. 

Referring  to  tig.  1,  the  positions  of  the  camera  stations  A and  A',  also  the  distance  A A\ may 
be  given,  and  two  photographs  containing  the  image  t of  an  object  1\  including  the  image  a'  of 
the  other  camera  station,  may  have  been  obtained  from  the  two  stations. 

630 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


631 


If  the  base  line  A A',  fig.  2,  be  laid  down  on  paper,  in  reduced  scale,  and  if  the  pictures  4/A  and 
M'  A',  fig.  3,  be  brought  into  the  same  relative  positions  with  reference  to  the  platted  line  which  they 
had  at  the  time  of  their  exposure  in  the  field,  the  position  T of  the  pictured  point  (with  reference 
to  the  platted  points  A and  A')  may  be  located  by  drawing  the  rays  A t and  A'  V to  their  inter- 
section. To  locate  the  platted  position  of  T the  horizontal  projections  of  the  rays  A t and  A' t' 
are  brought  to  their  intersection  on  the  platting  sheet,  fig.  4,  which  may  be  done  by  ascertaining 


M’ 

t 

c pc 

x'j/ 

r 

N' 

M ^ 

r 

' X 

p : 

t 

a1 

N 

the  proper  positions  of  the  lines  of  intersection  of  the  picture  planes  with  the  horizontal  platting 
plane  with  reference  to  A and  A'  (by  “orienting”  the  picture  traces). 

The  map  being  the  orthogonal  projection  of  the  terrene  in  horizontal  plan,  the  horizontal 
projections  of  the  perspectives  (or  picture  planes  exposed  in  the  vertical  plane)  will  appear  as 
straight  lines,  termed  “picture  traces,”  fig.  4. 

The  correct  orientation  of  the  picture  traces  forms  the  most  important  part  of  iconometric 

, ' T 


r,G.4- 


platting,  the  subsequent  location  of  picture  points  being  accomplished  by  bringing  the  horizontal 
projections  of  the  visual  rays — lines  of  direction — drawn  to  identical  points  to  their  corresponding 
intersections. 

I.  ORIENTING  THE  PICTURE  TRACES  ON  THE  WORKING  SHEET. 

(1)  A base  line  44',  measured  in  the  field,  has  been  platted  to  scale,  fig.  2,  and  two  pictures, 
4/A  and  M'N',  fig.  3,  had  been  obtained  from  the  camera  stations  A and  A1  respectively  by 
means  of  a surveying  camera.  The  focal  lengths  of  the  pictures  (=/  and  f respectively),  the 
positions  of  the  principal  points  (P  and  P'),  and  the  horizon  lines  may  also  be  given. 

It  is  desired  to  locate  T with  reference  to  44'  upon  the  working  sheet. 

The  distances:  AP=f;  A'P'  = f (fig.  4);  tP,  t'P',  Pa'  and  P'a  (to  be  measured  on  the  pictures 
4/A  and  4PA'  respectively)  and  the  line  44'  are  given. 

The  distances  Aa'  and  A' a may  be  found  graphically  (by  constructing  the  right-angle  triangles 
APa!  and  A' P'a),  or  they  may  be  computed  from  the  equations: 

Aa‘  = V(AP)2+  {Pa1)2 

A‘a  = V(A'P'f  + (P'a)2 

These  distances  are  now  laid  off  upon  AA'  from  A and  A'  respectively,  semicircles  are 
described  over  Aa'  and  A 'a,  and  two  circles  are  drawn  about  A and  A'  with /and  f respectively, 
as  radii. 


632 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY 


The  intersections  P and  P'  of  these  two  pairs  of  circles  locate  the  horizontal  projections  of 
the  principal  points  on  the  two  picture-traces,  the  latter  being  represented  by  the  tangents  Pa' 
and  P'a.  The  distances  x (=  Pt)  and  x'  ( — P't')  are  now  measured  on  the  pictures  and  laid  off  on 
the  tangents  as  indicated  in  fig.  2,  when  the  intersection  of  the  lines  drawn  from  A and  A' 
through  the  points  (just  found)  t and  t'  will  locate  the  horizontal  projection  of  T with  reference  to 
A and  A'. 

(2)  The  instrument  used  was  a camera  or  phototheodolite: 

In  this  case  the  angles  a and  a'  (fig.  2)  may  be  measured  directly  in  the  field. 

We  now  plat  the  angles  a and  a'  upon  the  base  line  AA‘  and  make  AP  = f and  A'P1  = f. 

The  perpendiculars  to  AP  and  A'P1  in  P and  P',  respectively,  will  represent  the  picture- 
traces  ( ta ' and  t'a)  in  correct  orientation. 

(3)  When  several  pictured  points  (triangulation  points)  and  the  base  line  are  given  on  the 
working  sheet,  the  orientation  of  the  picture-traces  upon  the  map-projection  may  be  accomplished 
as  follows  (fig.  5): 

pa 

/ \ 


\ 

/ \ 


The  rays  AB , AC , AD , and  A'B , A' C,  A'D  are  drawn  upon  the  iconometric  platting  sheet, 
the  points  B,  C,  and  D being  already  platted  on  the  same. 


M 1 

? 

9 

9 ! 9 

i • | 

a 

p c b a 

N 

Fig  6 


The  points  ft,  c,  P,  d,  and  a are  transferred  from  the  horizon  line  00'  of  the  negative  MN  (fig.  6) 
upon  the  perfectly  straight  edge  of  a strip  of  paper,  which  is  placed  upon  the  radials  drawn  lroin 
A (as  center)  to  the  points  P,  C,  />.  The  strip  is  now  moved  about  until 

ft  falls  upon  the  ray  AB 
c falls  upon  the  ray  AC 
d falls  upon  the  ray  AD 
a' falls  upon  the  line  AA' 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


633 


The  line  AP  should  now  be  perpendicular  to  the  straight  edge  of  the  paper  strip,  and  the  line 
bcda'  drawn  upon  the  working  sheet  (along  the  straight  edge  of  the  paper  strip)  will  represent  the 
oriented  picture-trace  of  MN- — 

AP  will  be  the  distance  line,  and 

P will  be  the  horizontal  projection  of  the  principal  point. 

The  same  having  been  done  regarding  the  point  A1  and  its  picture  M'JSf,  both  picture-traces 
will  be  oriented  and  the  positions  of  any  additional  points,  that  may  be  identified  on  both  pictures, 
may  be  located  by  platting  their  abscissae  (measured  on  the  horizon  lines  of  the  pictures,  regarding 
P as  the  origin  of  the  coordinates)  upon  the  picture- traces  on  the  proper  sides  of  the  principal 
points.  Lines  drawn  from  the  station  points,  A and  A' , through  such  corresponding  points  on 
the  picture- traces  will  locate  the  relative  positions  of  such  points  on  the  platting  sheet  by  their 
points  of  intersection. 

II.  ARITHMETICAL  DETERMINATION  OF  THE  PRINCIPAL  AND  HORIZON  LINES  ON  THE  PICTURES. 

In  the  preceding  it  had  been  assumed  that  each  perspective  was  provided  with  the  principal 
and  horizon  lines,  which  would  be  the  case  when  an  adjusted  surveying  camera  or  phototheodolite 


had  been  used  for  obtaining  the  pictures.  When  an  ordinary  camera  (with  provisions  to  maintain 
the  picture  plane  in  a vertical  position)  or  an  unadjusted  surveying  camera  is  used,  the  correct 
position  of  the  principal  and  horizon  lines  as  well  as  the  length  of  the  distance  line  (focal  length) 
must  be  ascertained,  which  may  be  accomplished  in  various  ways: 

(1)  Determination  of  the  principal  point  and  distance  line  of  the  perspective. — A plumb-bob, 
suspended  in  such  a way  that  the  plumbline  will  be  photographed  upon  the  negative,  may  serve 
to  establish  the  direction  of  the  principal  line  VV  (lig.  7)  upon  the  trial  plate. 

The  negative  may  also  contain  the  images  a,  b,  c,  . . . . of  three  or  more  points  A,  B , G , 

. . . . of  known  positions.  A line  hh  is  drawn  upon  the  negative  perpendicular  to  VY,  and 
the  straight  edge  of  a paper  strip  is  placed  upon  this  line.  The  pictured  points  a,  b,  c,  . . . . 

are  now  projected  upon  the  straight  edge  of  the  paper  by  drawing  parallels  to  YY  through  the 
points  a,  b,  c,  . . . . (lig.  7). 

After  having  drawn  radials  from  the.  platted  station  & to  the  points  A',  B',  C", 

the  paper  strip  is  adjusted  over  the  former  in  such  a way  that  the  image  projectious  a1,  b',  & will 
fall  upon  their  corresponding  radials,  when  the  position  (as  indicated  by  the  line  hh)  of  the  paper 
strip’s  edge  will  be  the  oriented  picture  trace.  If  we  now  draw  a line  (SP1)  from  the  platted 
station  S perpendicular  to  hh,  the  point  P'  will  be  the  horizontal  projection  of  the  principal  point 
P,  and  SP'  will  be  the  distance  line  (=f)  for  the  picture  MN. 


634 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


Whenever  the  positions  of  the  points  A,  B,  C,  . . . . with  reference  to  the  station  S are 
not  known,  it  will  become  necessary  to  observe  the  horizontal  angles  A SB,  BSC,  GSD,  . . . . 

instrumentally  from  the  station  S,  and  plat  the  same  upon  a sheet  of  paper  in  order  to  adjust  the 
paper  strip  upon  the  radials,  in  the  manner  just  described,  to  find  the  principal  point  and  distance 
line  (focal  length). 

(2)  Determination  of  the  position  of  the  horizon  line  on  the  perspective. — When  the  elevations 
AA',BB',CG',  ....  of  the  points  A,  B,  G,  ....  above  the  horizon  of  the  station  ((S') 
are  known,  the  position  of  the  horizon  line  ( oo ')  (fig.  8)  may  be  found  by  constructing  or  by 
computing  the  lengths  of  the  ordinates  aa ',  hb ' , cc',  ....  from  the  relations: 

aa' : AA'  = Sa' : SA' 
bb' : BB'  = Sb' : SB' 
c&:  GC‘  = Sc':  SC' 


whence 


aa1  = 


bb'  - 


Sa'.AA 1 
SA' 

Sb'.BB' 
— SB ~ 


= yl 

=y',  etc. 


A 


The  distances  Sa',  Sb',  Sc',  . . . are  taken  from  the  platting  sheet  (fig.  8)  and  the  distances 

SA1,  SB',  SC', as  well  as  the  differences  in  elevation  AA' , BB',  CC‘, 

are  known  (if  the  points  A,  B,  C,  . . . had  been  located  in  the  horizontal  and  vertical  sense 

with  reference  to  the  station  S). 

For  example: 

Difference  in  elevation  between  A and  A'  = 100m. 

Distance  of  A'  from  the  station  S = 1000m. 

Distance  Sa',  measured  on  the  platting  sheet,  — 0’5,n. 


m,  , , 0*5x100  a arm 

The  ordinate  aa'  = — 0-05m. 

The  horizon  line  {oo')  on  the  negative  will  be  50  mm.  vertically  below  (parallel  with  VV)  the 
pictured  point  a. 

The  direction  of  VV  {the  principal  line)  being  parallel  to  the  pictured  plumb  line,  this  distance 
aa'  is  laid  off  in  the  same  direction  below  a,  and  a line  oo',  drawn  at  right  angles  to  VV  through  a', 
will  locate  the  horizon  line.  The  ordinates  bb',  cc ',  ....  of  the  other  pictured  points  may 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


635 


well  serve  to  check  this  position  of  oo'.  The  horizon  line  will  be  the  tangent  to  the  arcs  described 
with  aa',  bl V,  cc' , ....  about  a,  b,  c,  . . . . respectively,  as  centers. 

The  principal  point  P,  may  now  be  transferred  to  the  negative  by  using  the  paper  strip,  and 
the  line  drawn  through  P perpendicular  to  oo'  will  be  the  principal  line  for  the  picture  MN. 

III.  GRAPHIC  METHOD  FOR  DETERMINING  THE  POSITIONS  OF  THE  PRINCIPAL  AND  HORIZON 

LINES  ON  THE  PERSPECTIVES. 

The  following  graphic  method  for  orienting  the  picture  trace  and  locating  the  principal  and 
the  horizon  lines  was  published  by  Prof.  F.  Schiffner  in  1887;  it  is  also  mentioned  by  Prof.  F. 
Steiner. 

Three  points,  A , B,  and  G (hg.  9),  may  be  given  with  reference  to  the  station  S upon  the 
platting  sheet. 

B 


From  S radials  are  drawn  through  A,  P,  and  C.  Through  a point  a on  the  ray  SA  a parallel 
to  SC  is  drawn,  and  the  distance  a'b'  (taken  from  the  negative  MN)  is  laid  off  from  a ( = ab\)  upon 
this  parallel,  while  the  distance  b'c'  is  laid  off  upon  the  same  line  from  b\  (=  b'xc\).  Parallels  to 
the  radial  $A  are  now  drawn  through  the  points  b\  and  c\  and  prolonged  to  intersect  the  radials 
SB  and  SC.  The  line  [li'li')  connecting  these  two  points  of  intersection  will  be  parallel  with  the 
direction  of  the  picture  trace. 

The  same  distances  a'b'  and  b'c ' (taken  from  the  negative)  are  laid  off'  upon  this  line  li'li'  from 
<h  (=  (hbz)  and  from  b2  ( = b2c2 ).  The  lines  drawn  through  these  points  b2  and  c 2,  and  parallel  with 
the  radial  SA,  are  brought  to  intersections  with  the  radials  SB  and  SC,  when  the  line  (hh)  passing 
through  these  intersections  will  represent  the  picture  trace  correctly  placed  (oriented)  with  reference 
to  S,  A,  B,  and  C. 

The  distance  SP  of  S from  hh  represents  the  distance  line  (focal  length)  of  the  picture  MN, 
while  the  point  P‘  will  be  the  horizontal  projection  of  the  principal  point  P. 

After  having  transferred  P'  (with  reference  to  a',  b',  and  &),  by  means  of  a paper  strip,  to  the 
negative  MN,  a parallel  to  VV,  drawn  through  the  transferred  point  P,  will  locate  the  principal 
line  upon  the  negative. 

The  horizon  line  may  now  be  located  in  the  same  manner  as  shown  under  II,  2,  adopting  the 
graphic  solution. 


636 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


IV.  THE  FIVE-POINT  PROBLEM  (BY  PROFESSOR  STEINER). 

In  the  methods  just  described  it  had  been  assumed  that  the  position  of  the  camera  station 
was  known  with  reference  to  the  surrounding  points  A,  B,  G 

In  case  the  panorama  pictures  were  taken  from  a camera  station  of  unknown  position  and  a 
series  of  known  points  are  pictured  upon  the  panorama  views,  the  position  of  the  camera 
station  may  be  found  (with  reference  to  the  surrounding  points  of  known  positions),  and  the  orien- 
tation of  the  picture  trace  may  be  accomplished  by  means  of  Prof.  F.  Steiner’s  so-called  “ five- 
point  problem”  (fig.  10),  if  one  of  the  views  contains  the  pictures  of  five  or  more  points  of  known 
positions. 

The  panorama  view  MN  may  contain  the  images  a,  b , c,  d , and  e of  the  points  A,  B,  C, 
D,  and  E (already  plotted  upon  the  working  sheet),  and  also  the  picture  of  a suspended  plumb 
line  or  other  vertical  (or  horizontal)  line. 


a 


The  points  a , b , c,  d , and  e of  the  negative  are  again  projected  upon  the  straight  edge  of  a 
paper  strip  = a b',  &,  d',  and  e'. 

ttadials  are  now  drawn  from  one  (A)  of  the  five  plotted  points,  as  a center,  to  the  other  four, 
B , (7,  D,  and  E.  The  marked  paper  strip  is  then  placed  over  the  radials  in  such  a way  that 

b'  falls  upon  AB,  d'  falls  upon  AD , e'  falls  upon  AE, 

when  the  strip  will  have  the  position  a\,  bt,  C\,  d\,  6i-  The  line  drawn  through  A and  «i  (the  latter 
transferred  by  means  of  the  strip)  will  be  the  tangent  in  A to  the  ellipse  (passing  through  A , 
B , 77,  E and  through  the  station  point  S). 

The  paper  strip  is  now  placed  over  the  radials  AB , AC,  and  AD,  so  that 

b'  falls  upon  AB,  d falls  upon  A C,  d'  falls  upon  AD, 

when  the  strip  will  have  the  position  a2  b>  c2  dt  c2,  and  the  lino  A n,  will  be  the  tangent  in 
A to  the  ellipse  E2  (passing  through  the  points  A,  B,  C,  D and  the  station  point  8). 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


637 


The  position  of  the  station  point  S on  the  working  sheet  (with  reference  to  the  five  points  A, 
B , G’,  D,  and  E)  will  be  identical  with  the  point  of  intersection  of  the  two  ellipses  Ex  and  E2. 

(1)  Determination  of  the  principal  point  and  distance  line  in  the  perspective. — The  distance  line 
and  the  principal  point  are  now  found  by  drawing  the  radials  SA,  SB , SC,  SD,  and  SE,  and 
placing  the  paper  strip  over  these  in  such  a way  that 

a'  falls  upon  SA,  b'  falls  upon  SB,  & falls  upon  SC,  d'  falls  upon  SD,  e'  falls  upon  SE, 


which  position  is  indicated  by  the  line  HH.  The  perpendicular  upon  HH  passing  through 
S (=  SB)  is  the  distance  line  and  P is  the  principal  point  projected  into  horizontal  plan,  which 


/ 


may  now  be  transferred  to  the  picture  by  means  of  the  paper  strip  in  order  to  locate  the  principal 
line  in  a similar  manner  to  that  mentioned  in  the  preceding  pages. 

(2)  Simplified  construction  for  locating  the  camera  station  by  means  of  the  five-point  problem. — The 
preceding  method  is  rather  complicated,  but  Professor  Schiffner  devised  the  following  construc- 
tion (fig.  11),  in  which  the  drawing  of  the  ellipses  Ex  and  E2  is  avoided: 

The  same  five  points,  A,  B,  C,  D,  and  E,  with  their  images  a,  b,  c,  d,  and  e,  on  one  plate  AIN, 
may  be  given. 

The  two  lines,  b3  B and  bt  B,  tangent  in  B to  the  two  ellipses  Ex  and  E<,  respectively,  are  located 
precisely  in  the  same  manner  as  the  two  tangents  ax  A and  a2  A were  found  for  the  point  A. 


638 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


The  intersections  i?i  and  B2  of  the  tangent  pairs  ax  A,  b3  B and  a2  A , 64  B (belonging  to  tbe 
ellipses  Ex  and  E2,  respectively)  are  situated  upon  a line  Qx,  forming  one  side  of  the  polar  triangle 
QxT,  common  to  both  ellipses.  This  line  Qx  intersects  the  diagonal  AD  in  x and  the  quadrilateral 
side  BD  in  Q , and  the  lines  drawn  through  Q from  A and  through  x from  B will  intersect  each 
other  in  the  fourth  point  of  intersection  (8)  of  the  two  ellipses. 

The  quadrilateral  ABDS,  obtained  by  connecting  the  four  points  of  intersection  of  the  two 
ellipses,  has  the  point  x as  the  intersection  of  its  diagonals.  By  prolonging  the  sides  BD  and  A 8 
to  their  point  of  intersection  Q and  the  sides  AB  and  SD  to  their  point  of  intersection  T , the 
three  diagonal  points  QxT  will  form  the  polar  triangle  common  to  the  two  ellipses. 

Also  this  method  remains  complicated  and  requires  many  lines  to  be  drawn  before  the  picture 
trace  and  the  camera  station  ( S)  may  be  plotted. 

(3)  Special  application  of  the  Jive-point  problem  for  the  case  when  the  Jive  points  range  themselves 
into  a triangle. — The  application  of  the  “five-point  problem”  becomes  very  much  simplified,  how- 
ever, for  the  special  case  when  the  five  points  range  themselves  into  a triangle,  of  which  two  sides 
(AC  and  CE)  contain  three  points  each  (tig.  12). 

c 


If  we  now  place  the  strip  of  paper  upon  the  radials  drawn  from  A,  so  that 

e'  falls  upon  AE,  d‘  falls  upon  AD,  c'  falls  upon  AC , 

it  will  have  the  position  a2  b2  c2  d2  e2,  and  the  first  ellipse  (EJ  will  resolve  itself  into  the  lines  CE 
and  Aa2. 

If  we  now  place  the  paper  strip  a'  b'  & d'  e 1 upon  the  radials  drawn  from  E to  A,  B and  C, 
so  that  a ' falls  upon  EA,  b'  upon  EB,  and  c‘  upon  EC,  it  will  assume  the  position  a,  bx  cy  dx  ex,  and 
the  second  ellipse  (E2)  will  have  resolved  itself  into  the  lines  AC  and  Eex. 

The  intersection  8 of  the  two  lines  Aa2  and  Ee]  will  locate  the  station  point  with  reference  to 
the  five  given  points,  and  by  placing  the  paper  strip  upon  the  radials  8A,  SB,  SC,  8D,  and  SE  in 
such  a way  that  a1  falls  upon  SA,  b‘  upon  SB,  etc.,  its  edge  will  locate  the  picture  trace. 

(4)  To  find  the  elevation  ( x ) of  a camera  station  (S)  that  has  been  located  by  means  of  the  “ five- 
point  problem .” — In  order  to  ascertain  the  elevation  of  the  unknown  station  S,  platted  after  one 
of  the  preceding  methods,  it  will  become  necessary  to  know  the  elevations  of  at  least  two  ot  the 
five  points. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


639 


Let  the  elevation  of  the  station  8 fig.  8 be  designated  by  x. 

The  elevation  of  A = H and  of  B = Ex.  The  ordinates  aa'  = y and  bb'  = yx. 
From  the  relation  8' a x'  : S'Ai  = aa'  : AA' ; 

or  „ 

8a'  : 8 A'  = y : [H  — x) 

we  find 

y—  (H  — x ) and 

V\  — gfi/  (-®i  x)m 

The  difference  between  y and  y\  may  be  measnred  on  the  negative,  hence 

V - 2/i  = »» 


is  known,  and  the  value  for^  may  be  found  from  the  equation 


y — yi  = (H  — x) 


8a'  „ M 

SA'  ~ ~ x)  SB'  ~ 


The  values  for  8a',  SA',  Sb',  and  SB1  may  be  taken  directly  from  the  platting  sheet,  while 
those  for  H and  if,  are  found  in  the  triaugulation  records. 

If  we  write  the  above  equation  in  the  general  form — 

H — x Hx  — x 


the  elevation  x of  the  camera  station  8 may  be  computed  from — 

vino  — Ho  + Hxii 


x = 


n — o 


The  numerical  values  for  the  ordinates  y and  ?/i  (locating  the  position  of  the  horizon  line  on  the 
perspective)  may  now  be  computed  from  the  equations — 

H-x 

y — and 


E-x 

?/i=  0 

V.  THE  THREE-POINT  PROBLEM. 

If  the  triaugulation  points  are  not  sufficiently  close  together  that  five  or  more  points  may  be 
pictured  on  one  perspective,  and  if  stations  are  occupied  with  the  camera  that  are  not  connected 
with  the  trigonometric  survey,  it  will  become  necessary  to  employ  other  means  to  determine  the 
position  of  the  camera  station  with  reference  to  the  surrounding  triaugulation  points. 

In  order  to  connect  the  camera  station  with  the  triaugulation  system  by  direct  measurements 
and  observations,  made  at  the  camera  station,  it  will  be  requisite  that  at  least  three  triaugulation 
points  be  visible  from  such  station,  unless  the  location  of  the  camera  station  is  to  be  made  by 
observations  made  from  other  stations.  In  the  latter  case  the  occupation  of  two  (better  three) 
triangulation  points,  if  favorably  located,  would  suffice  to  establish  the  (“concluded”)  position  of 
the  camera  station. 

The  determination  of  the  position  of  an  occupied  point  by  observing  upon  three  fixed  and 
known  points  is  generally  known  as  the  “ three  point  problem,”  “station  platting,”  “station 
pointing,”  or  “ Pothenofs  method,”  although  Suellius  had  used  the  same  method  in  his  trigono- 
metric work  in  the  Netherlands  in  the  second  decade  of  the  seventeenth  century.  Let  A , B,  and 
C,  fig.  13,  be  the  three  points,  the  positions  of  which  are  known.  A fourth  undetermined  point  8 


640 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


may  have  been  occupied  from  which  the  horizontal  angles  A S B = M and  B S C = N may  have 
been  observed  instrumentally.  The  position  of  S with  reference  to  A,  B,  and  C may  then  be  ascer- 
tained in  various  ways. 

(1)  Using  the  three-arm  protractor  ( mechanical  application  of  the  three-point  problem). — The 
simplest  (and  crudest)  method  is  purely  mechanical  in  its  application.  The  two  horizontal  angles 
M and  N are  laid  off  upon  a three-arm  protractor  (“station  pointer”),  or  upon  a piece  of  tracing 
paper,  moving  the  three  radials  SA,  SB , and  SC  over  the  three  fixed  and  platted  points  A , B , and  C 
until  the  three  radials  SA,  SB,  and  SC  bisect  their  corresponding  points  A , B,  and  C.  Holding 
the  two  angles  M and  N unchanged  in  this  position,  the  point  S is  transferred  to  the  working  sheet. 

(2)  Graphic  solution  of  the  three-point  problem — 

(a)  Using  the  so-called  “ two-circle  problem. v — Theoretically  the  best  graphic  method  is  that 
which  locates  the  position  of  the  fourth  point  S,  fig.  13,  as  the  intersection  of  two  circles,  one 
passing  through  A and  B and  having  all  angles  of  circumference  = A SB  = M over  AB  that  may 
be  drawn  over  the  line  AB  as  chord,  the  other  circle  passing  through  B and  C and  having  over 
BC  as  chord  all  angles  of  circumference  equal  to- BSC  = JV. 


B 


From  the  platted  triangle  side  AB  we  lay  off  at  A and  B the  angles  BAG  and  ABC i each 
equal  to: 


180  - 2 {A SB) 

9 


= 90°  - A SB  = 90°  - ill 


and  about  the  point  c ,,  thus  obtained,  a circle  ABS  is  described  with  the  radius  = cxA  = cxB. 
The  observed  angle  ASB  = M will  then  be  an  angle  of  circumference  over  AB , and  the  point  S 
will  be  located  somewhere  on  the  arc  over  the  chord  AB. 

By  means  of  the  angle  BSC  = N a second  circle  BCS  is  described  over  the  triangle  side  BC, 
m a similar  manner,  about  c2  as  center  with  the  radius  cxB  = cxC.  The  observed  second  angle 
BSC  = N will  be  an  angle  of  circumference  over  the  chord  BC,  hence  the  point  S will  be  situated 
also  upon  the  arc  over  the  chord  BC  and  the  true  position  of  8 is  at  the  point  ot  intersection  S of 
the  two  circles. 

(b)  Using  the  method  of  Bohnenberger  and  Bessel. — The  following  constructive  method  (devised 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


641 


by  Bolinenberger  and  Bessel)  is  readily  applied  and  of  a very  simple  character,  fig.  14.  If  we 
describe  a circle  through  two  of  the  three  given  points  A and  B and  the  station  S as  the  third 
point  the  angles 

ASB  = ACB  = M and 

BSC  = BAG  — N (being  angles  of  circumference  upon  the 


same  arcs  AD  and  DC  respectively). 

Hence,  if  we  lay  off  the  observed  hori- 
zontal angle  M on  the  base  line  AC  at  C 
and  the  other  horizontal  angle  Aon  AC  at 
A , the  point  of  intersection  D of  their  con- 
vergent sides  CD  and  AD  will  be  on  the 
Hue  connecting  the  third  point  B and  the 
platted  station  S.  After  having  thus  found 
the  direction  of  the  line  DB  the  position 
of  8 on  the  line  DB  may  be  found  as  fob 
lows: 

At  any  point  x of  the  line  DB  the  ob. 
served  angles  M and  A are  laid  off  to  either 
side  of  DB,  in  the  sense  in  which  they  were 
observed.  Lines  AS  and  CS  drawn 
through  A and  C parallel  to  xy  and  xz, 
respectively,  will  locate  the  position  of  the 
station  S (upon  DB)  with  reference  to  the 
three  points  A,  B , and  C. 

This  construction  is  only  recommended 
when  BD  is  sufficiently  long  (in  fig.  14  it  is 
evidently  too  short)  to  admit  of  a correct 
prolongation  of  its  direction  toward  8. 

The  picture  trace  containing  the  hori- 
zontal projections  of  the  pictured  points  a , 

b,  and  c may  now  be  oriented  in  the  known  manner  by  adjusting  the  paper  strip  over 
SA,  SB,  and  SC. 


the  radials 


VI.  ORIENTATION  OF  THE  PICTURE  TRACES,  BASED  UPON  INSTRUMENTAL  MEASUREMENTS 

MADE  IN  THE  FIELD. 

When  no  points  are  known  of  the  area  to  be  mapped  phototopographically  the  elements  of 
the  perspective  (horizon  line,  principal  point,  and  distance  line)  can  no  longer  be  ascertained  from 
the  photograph  alone,  but  instrumental  observations  will  have  to  be  resorted  to.  This  method, 
having  been  adopted  by  Capt.  E.  Deville,  will  be  described  in  Chapter  III,  II,  3,  in  connection 
with  the  Canadian  method. 


VII.  RELATIONS  BETWEEN  TWO  PERSPECTIVES  OF  THE  SAME  OBJECT  VIEWED  FROM  DIFFERENT 
STATIONS  (“KERNELPOINTS”  AND  “ KERNELPLANES  ”). 

A more  generalized  application  of  photogrammetric  methods  has  been  inaugurated  since 
Prof.  G.  Hauck  published  his  investigations  and  results  regarding  the  relationship  existing 
between  systems  of  three  lines,  each  of  the  latter  being  in  a different  plane.  (“Theorie  der  tri- 
linearen  Verwandtschaft  ebener  Systeme,”  Journal  fiir  reine  und  angewandte  Mathematik, 
herausgegeben  von  L.  Kronecker  und  A.  Weierstrass,  1883,  Bd.  95.) 

The  practical  value  of  Professor  Hauck’s  deductions  had  been  tested  by  the  students  attend- 
ing his  lectures  in  1882  during  the  exercises  which  are  connected  with  the  course  in  descriptive 
geometry  at  the  Technical  High  School  in  Berlin  (Charlottenburg). 

(1)  Kernelpoints  and  Icernelplanes. — In  his  discussion  of  the  relationship  existing  between  two 
perspectives  of  the  same  object  taken  from  different  stations,  Professor  Hauck  has  evolved  some 
0584 41 


642 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


properties  which  may  be  very  useful  and  of  value  in  iconometric  platting.  The  principal  law 
involved  in  the  application  of  photogrammetry  may  be  stated  as  follows : 

If  two  projections  (perspectives  or  photographs)  of  the  same  object  are  projected  by  perspective  rays  emanat- 
ing from  the  “kernelpoints”  (“kernpunkte ”)  as  centers  the  liue  of  intersection  of  the  two  planes  of  projection 
(picture  planes)  will  he  their  perspective  axis. 

With  the  aid  of  this  law  the  projection  on  a third  plane  of  an  object  may  be  deduced  from  the 
given  projections  on  two  planes  of  the  same  object.  Or,  for  our  case: 

If  two  photographs,  MN  and  M'N ' , taken  from  two  stations  S and  S'  (and  representing  the 
same  object),  are  given,  the  orthogonal  horizontal  projection  (ground  plan)  of  tbe  same  object  may 
be  constructed  therefrom. 

Professor  Hauck’s  methods  are  also  applicable  to  photographs  obtained  when  the  plate  was 
exposed  in  an  inclined  position.  In  order  to  illustrate  the  connection  existing  between  two 
different  perspectives  of  the  same  object,  we  will  refer  to  tig.  15,  representing  the  simple  case 

where  the  two  perspective 
planes  (MN  and  M'N1)  are 
vertical. 

Let  8 and  S'  represent 
the  two  camera  stations  (cen- 
ters of  projection  or  points  of 
view  for  the  vertical  picture 
planes  MN  and  M'N'),  s'  the 
picture  of  S'  in  MN,  s the  pic- 
ture of  S in  M1  N ID  the  line 
of  intersection  of  the  two  pic- 
ture planes  MN  and  M1  N ' , a 
image  of  the  point  A in  MN, 
o / image  of  the  point  A in 
M'  N'. 

The  two  pictured  points 
s and  s'  are  the  so-called  “ker- 
nelpoints” (kernpunkte),  and 
any  plane  (“  kernelplane”) 
passing  through  the  line 
(base  line)  SS'  will  contain 
the  “kernelpoints”  s and  s'. 

The  position  of  the  “ker- 
nelpoints” may  be  found 
graphically  bypassing  a plane 
(“kernelplane”)  through  the 
two  stations  and  a third  point  A (pictured  in  both  planes  MN  and  M'  N'),  which  will  intersect 
the  first  picture  plane  MN  in  the  line  as'  and  the  picture  plane  M'  N'  in  sa'.  Then  the  following 
conditions  will  prevail: 

1.  The  lines  of  intersection  as'  and  a' s will  intersect  the  line  ID,  in  one  point  (D,). 

“.  The  pictures  a and  a'  of  the  point  A will  be  on  the  lines  as'  and  a' s. 

3.  The  lines  as'  and  a' s will  pass  through  the  pictures  (s'  and  s)  of  the  two  camera  stations 
(S'  and  S). 

The  lines  S'  A,  SA,  SS',  as',  and  a' s being  situated  in  the  “ kernelplane”  M2  N2,  all  lines  as' 
(for  all  points  of  the  object  pictured  in  MN)  will  pass  through  the  picture  s'  (“kernelpoints”)  of 
the  second  camera  station  S',  and  all  lines  a' s (for  all  points  of  the  object  pictured  in  M'  N')  will 
pass  through  the  picture  s of  the  first  camera  station  S.  Furthermore,  all  lines  (as1  and  a' s) 
joining  the  two  perspectives  (pictures)  of  identical  points  (A)  with  the  corresponding  “kernel- 
points”  (s'  and  s)  will  intersect  the  line  of  intersection  (ID)  of  the  two  picture  planes  (MN  and 
M'  N')  in  the  same  point  (D). 

Therefore,  if  two  photographs  (MN  and  M'  N')  of  the  same  object  (A)  contain  the  pictures 
(s'  and  s)  of  their  reciprocal  stations  (S'  and  S),  conditions  peculiarly  adapted  for  the  facilitation 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


643 


of  the  iconometric  constructions  will  arise,  inasmuch  as  such  pictured  stations  ( s and  s')  will  be 
“kernelpoints.” 

The  line  of  intersection  {ID)  of  the  two  picture  planes  {MN  and  M'  Nj  may  also  play  an 
important  part  in  the  iconometric  platting',  not  only  for  pictures  exposed  in  vertical  planes,  but 
even  more  so  when  they  are  exposed  in  inclined  planes. 

If  two  pictures  MN  and  M'  N'  are  giveu  (in  fig.  16  their  traces  are  represented  as  HR  and 
E'  R‘ , respectively)  representing  the  same  object  (viewed  from  two  stations  8 and  S'),  then  the 
pictures  s and  s'  (“  kernelpoints”)  of  the  reciprocal  camera  stations  may  be  located  upon  the 
picture  planes  by  construction  (if  they  are  not  shown  in  the  field  of  the  pictures),  as  shown  in 
fig.  10. 

The  horizontal  projections  (s,  and  sj)  of  the  “ kernelpoints ” (s  and  s')  are  identical  with  the 
points  of  intersection  of  the  base  line  {88')  and  the  pictures  traces  (HII and  H'H').  The  horizontal 
projections  of  the  line  of  intersection  (TO,  fig.  15)  of  the  two  picture  planes  {MN  and  M'  N')  will 
be  represented  by  the  point  of  intersection  {i)  of  the  two  picture  traces  {HR  and  R'  R'). 

Hence,  if  we  revolve  the  picture  planes  about  their  ground  lines  until  they  fall  within  the 
horizontal  plane  of  the  ground  plan,  the  line  JO,  fig.  15  (common  to  both  picture  planes),  will 
be  represented  by  the  lines 
i(I ),  fig.  16,  and  the  “kernel- 
points”  s and  s'  of  the  re- 
volved planes  will  fall  upon 
the  lines  sjs)  and  s'js'),  re- 
spectively. (These  lines  are 
perpendiculars  upon  the  pic- 
ture traces  {HR  and  H'H') 
in  the  horizontal  projections 
of  the  “kernelpoints”.) 

To  find  the  lengths  «i(s) 
and  s'i{s')  (ordinates  of  the 
“kernelpoints”  in  the  pic- 
ture planes),  perpendiculars 
are  erected  in  8 and  8',  fig. 

16,  and  their  lengths  are 
made  equal  to  the  elevations 
of  the  respective  camera 
horizons  above  the  ground 
plane  = S(S)  and  8' {S'),  re- 
spectively. The  line  {S){8'), 
connecting  the  camera  sta- 
tions 8 and  S'  (in  fig.  16  the 
vertical  plane  passing  through 
the  camera  stations  S and  8'  has  been  revolved  about  the  horizontal  projection  of  the  base  line  8 S' 
until  it  coincides  with  the  horizontal  ground  plane)  will  iutersect  the  lines  s,(.sj  and  s'i(s')  (which 
are  perpendicular  to  the  horizontal  projection  of  the  base  line  in  the  “kernelpoints”  s,  and  s',), 
and  the  lengths 


o' 

0) 


Fig.  16 


In  this  mauner  the 


Si(s)  and  s'i{s')  will  equal  the  ordinates  of  the  kernelpoints. 

“kernelpoints”  may  be  located  in  the  picture  plane  of  any  photograph. 

(2)  Use  of  the  line  of  intersection  {ID.)  of  tic  o picture  planes  {MN  and  M'N')  which  show  identical 
objects  viewed  from  two  different  stations  (s  and  s'). — If  a series  of  characteristic  points  of  the 
terrene,  pictured  in  a vertical  picture  plane  MN,  fig.  17,  are  connected  with  the  “kernelpoint”  s 
by  straight  lines,  these  will  (when  prolonged)  intersect  the  line  ID,  and  if  the  pictures  of  the 
identical  points  in  the  vertical  picture  plane  M 'N'  are  joined  with  the  “kernelpoint”  s',  and  if  these 
lines  are  likewise  prolonged  to  intersect  the  line  {ID),  forming  the  intersection  of  the  two  picture 
planes  {MN  and  M'N'),  the  series  of  intersections  of  ID  with  the  first  group,  belonging  to  MN, 
will  be  identical  with  the  intersections  of  ID  with  the  second  group  of  lines,  belonging  to  M'N'. 

If  we  now  imagine  the  line  ID,  provided  with  a scale  of  equal  parts,  with  zero  in  the  ground 
plane  GG,  fig.  17,  lines  drawn  through  the  “kernelpoints”  and  identical  points  of  objects  pictured 


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UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


in  both  picture  planes  (MN  and  M'N')  will  intersect  identical  points  of  the  scale.  The  space 
(0 O')  intercepted  on  the  scale  by  the  horizon  lines  of  the  two  picture  planes  will  represent  the 
difference  in  elevation  between  the  two  camera  stations  ( S and  S').  This  scale  may  be  drawn  to 
show  on  both  lines  I. Q of  the  pictures  when  separated. 

The  picture  (photograph)  itself  frequently  may  not  be  sufficiently  extended  to  contain  the  line 
ID,  in  which  case  the  scale  may  still  be  utilized  by  laying  it  oft'  on  a line  xx"  on  picture  MN  and 
on  a line  zz"  on  picture  M'N',  where  xx"  and  zz"  are  parallel  with  the  line  of  intersection  (ID)  of 
the  two  picture  planes  MN  and  M'N'  and  as  long  as  the  following  relation  remains  fulfilled: 

sD  : sx'  = s'D  : s'z1 

For  a second  point  B pictured  as  b and  b'  on  the  two  picture  planes  MN  and  M'N',  respectively, 
the  following  proportions  must  stand  : 

s(3  : sx o = s'/3  : s'z„ 

From  the  similarity  of  the  triangles  sxnx',  s/3D , s'z()z',  and  s'  (3D,  we  find: 

xnx'  — znz' 

((3D  being  common  to  both  triangles  s(3D  and  s'  (3D),  which  means  the  spaces  on  the  scales  xx"  and 


zz"  are  the  same  in  numerical  value.  The  two  scales  (or  one  of  them)  may  also  be  placed  beyond 
,s.  an(i  s' — for  example,  at  tt" — in  which  case: 

s(3  : st0  — s(3  : sx0 
= s' (3  : s'zo 

when  the  scale  tt"  should  be  read  in  the  directions  from  V toward  tn.  It  may  generally  be  stated 
that  the  scales  should  be  placed  parallel  to  ID  and  at  distances  from  the  “ kernelpoints”  in 
proportion  to  the  distances  from  the  latter  to  the  line  of  intersection  of  the  picture  planes,  their 
correct  positions  being  best  found  graphically  from  the  horizontal  projection  or  from  the  ground 
plan.  To  avoid  the  obscuring  of  details  on  the  photographs  it  is  recommended  to  draw  these  scales 
outside  of  the  picture  proper. 

To  find  the  best  position  of  the  second  scale  on  the  second  picture,  graphically,  after  the 
position  for  the  first  scale  on  the  first  picture  has  been  decided  upon,  we  will  again  refer  to  tig.  1G, 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


645 


where  EH  and  H'H'  = picture  traces,  S and  S'  = horizontal  projections  of  the  camera  stations,  V 
and  P‘  — traces  of  the  principal  lines  / / and  /(/',  and  h = selected  positions  for  the  first  scale. 

To  find  the  corresponding  position  of  the  second  scale,  draw  a line  hh1  parallel  to  88'  through  h, 

s'ii  : s'Oi  = Sii  : sji1 

whence  sji'  = distance  of  the  second  scale  from  the  “keruelpoint”  in  the  second  picture  plane. 

The  conditions  and  relations  just  described,  and  first  discussed  by  Prof.  G.  Hauck,  may  often 
serve  with  advantage  in  iconometric  platting  (in  the  following  we  will  refer  to  them  again). 

For  example:  If  we  consider  the  case  of  a straight  line  Z,  fig.  18,  shown  on  MN  as  l,  of 
which,  however,  oidy  the  short  piece  l'  is  pictured  on  M'W,  and  it  is  desired  to  locate  a point  x , 
identified  on  l in  JOT,  but  falling  on  the  prolongation  of  V outside  of  the  picture  limit  of  M'N ', 
we  may  proceed  as  follows : 

The  pictured  point  x on  / in  MN  is  connected  with  the  “kernelpoint”  (s')  and  this  line  (s')  x 
is  prolonged  to  intersect  Ii  in  (x).  After  transferring  this  point  ( x ) to  the  line  i I of  the  second 


picture  plane  M1  A'  to  ((x)),  the  latter  point  is  connected  with  the  “kernelpoint”  (s),  and  the 
intersection  of  ((*))  ( s ) and  line  V will  be  the  point  sought,  x ',  of  the  prolonged  line 

VIII.  TO  PLAT  A FIGURE,  SITUATED  IN  A HORIZONTAL  PLANE,  ON  THE  GROUND  PLAN  BY 

MEANS  OF  ITS  PERSPECTIVE. 

In  topographic  surveys,  figures  in  level  planes  are  not  frequently  dealt  with,  except  when 
locating  the  outlines  of  lakes  and  marshes,  including  coast  lines,  and  the  simplest  way  to  plat 
these  would  be  to  expose  photographic  plates  (held  in  a horizontal  position)  from  a balloon  at 
points  of  known  positions  and  at  identical  or  known  elevations. 

The  platting  of  such  figures,  when  photographed  on  vertically  exposed  (also  inclined)  plates 
from  stations  higher  than  the  figure’s  plane,  will  also  be  an  easy  matter.  It  may  even  be 
accomplished  if  but  one  view  of  such  figure  had  been  obtained  from  only  one  station  (of  a known 
position),  provided  the  difference  in  elevation  between  the  camera  station  and  the  figure’s 
(horizontal)  plane,  the  principal  point,  and  the  focal  length  of  the  view  are  known. 

With  reference  to  fig.  19:  HE  — Horizon  plane  of  the  camera  station  8 , M N = Picture 
plane  (vertical),  G G = Ground  plane  or  horizontal  plane  coinciding  with  the  surface  of  the  lake 
ABC  I),  8 S0  = h = difference  in  elevation  between  the  camera  station  8 and  the  surface  of  the 
water  in  the  lake  A B C D. 


646 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


From  the  picture  abed  (of  the  lake  A B C D)  with  focal  length  = 8P  and  known  difference 
in  elevation  = li  the  horizontal  projection  of  the  lake  A B C T)  is  to  be  plotted. 

The  ground  line  0„  0o'  (intersection  of  ground  plane  G G and  picture  plane  M N)  is  drawn 
through  P0  parallel  to  the  horizon  line  O O'  (P  PQ  = h,  measured  in  the  platting  scale).  If  we  now 
project  the  pictured  points  a,  b , c,  and  d upon  0o  0o‘  = a0,  b0,  c,„  and  d0,  and  draw  radials  from  the 
platted  station  80  through  the  points  a0,  b0,  cQ,  and  d0,  they  will  pass  through  the  points  A,  B,  (7? 
and  I)  (which  are  to  be  platted),  and  the  latter  could  be  located  if  their  distances  from  S0  were 
known. 

We  now  regard  the  vertical  plane,  passing  through  the  camera  station  8 and  pictured  point  a, 
which  intersects  the  ground  plane  in  the  line  80  a0  or  in  80  A.  From  the  similar  triangles  8 S0  A 


and  a a0  A we  can  find  the  distance  8„  A (the  horizontal  distance  from  the  camera  station  to  the 
point  sought,  A)  either  graphically  or  arithmetically. 

When  the  vertical  plane  88nA  is  revolved  about  S0A  until  it  coincides  with  the  ground  plane 
GG,  the  points  8 and  a will  assume  the  positions  ( 8 ) and  (a)  respectively,  in  the  ground  plane,  and 
the  line  connecting  (8)  and  (a)  will  pass  through  the  point  A of  the  lake.  Hence,  A may  be 
located  in  the  ground  plan  as  the  intersection  of  (8)(a)  with  8oa0. 

The  same  may  be  done  for  the  points  B , (7,  and  D by  revolving  the  vertical  planes  S8nB, 
SS0C , and  88, J)  about  S0b0,  S0c0,  and  S0d0,  respectively,  into  the  ground  plane  to  locate  the 
positions  of  J3,  C , and  JJ. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


047 


To  avoid  a multiplicity  of  lines  on  the  working  or  platting  sheet,  these  constructions  are 
preferably  made  on  a separate  sheet  of  paper,  and  the  following  construction  may  be  adopted : 


The  vertical  planes  80a0,  S„b0 , 80cn , and  80d0  may  be  revolved  about  88„  as  axis  until  they  all 
coincide  with  the  principal  plane  880  PP0  (fig.  20),  where  the  paper  surface  may  represent  the 
principal  plane. 

HH  = trace  of  the  horizon  plane  in  the  principal  plane. 

MN  — trace  of  the  picture  plane  in  the  principal  plane. 

GG  = trace  of  the  ground  plane  in  the  principal  plane. 

S80  — difference  in  elevation  between  the  station  8 and  the  ground  plane  (surface 
plane  of  the  lake  ABCH),  measured  in  the  platting  scale. 

SP  = 80P0  = true  length  of  the  focal  distance  for  the  photograph  MN. 

The  radials  80a0,  Sob0 , Snc0,  and  80d0  are  laid  off  upon  the  line  GG  from  80.  The  verticals 
(«.„)(«),  (&„)(&),  (c0)(c),  and  (d0)(d)  are  made  equal  to  the  ordinates  aa0,  bb0,  ccn,  and  dd0  (measured  on 
the  picture).  Eadials  drawn  from  8 through  (a),  ( b ),  (c),  and  (d)  will  cut  off  on  the  line  GG  the 
horizontal  distances  S0(A),  80(B ),  S0(C),  and  S0(D ),  equal  to  the  horizontal  distances  $„A,  SUB, 
SQC , and  80L>,  measured  in  the  platting  scale.  If  these  distances  are  laid  off  upon  the  radials 
Sna0,  80b0,  *S'(Jc0,  and  8„d0  the  positions  of  the  characteristic  points  A,  />’,  C,  and  T)  of  the  lake  will 
be  platted  in  the  scale  of  the  map  with  reference  to  the  ground  line  0o0'0  (which  on  the  platting 
sheet  is  identical  with  the  picture  trace)  and  the  platted  station  8„. 

The  same  result  may  be  arrived  at  by  utilizing  the  orthogonal  projection  of  the  points  «,  b , c, 
and  d and  A,  B,  C,  and  I)  in  the  principal  plane,  instead  of  revolving  the  vertical  planes  into  the 
principal  plane. 

With  reference  to  fig.  21:  PP  = Principal  plane,  MN  = Picture  plane,  IIH  = Horizon  plane 
(containing  camera  station  S ),  GG  = Ground  plane  or  surface  plane  of  the  lake. 

If  we  draw  the  radials  80a0,  8ob0,  8oc0 , and  S0d0  from  80  (orthogonal  projection  of  8 in  GG) 
through  the  orthogonal  projections  a0,  b0,  c0,  and  d0  of  the  pictured  points  a,  b.  c,  and  d on  the 
ground  line  G„0,/,  the  points  sought  will  be  situated  upon  those  radials. 


648 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


If  we  now  project  the  points  a,  b,  c,  and  d (in  the  picture  plane)  upon  the  principal  line  = a, 
yS,  y,  and  6,  the  radials  Sa,  S/3,  Sy,  and  S8,  drawn  in  the  principal  plane  PP,  will  locate  the 


points  a0,  (30,  y0,  6„  upon  the  line  S0P0  (in  the  ground  plane),  they  are  the  orthogonal  projections 
of  the  points  A,  B , C,  and  D in  GG  upon  *S’0Pn.  The  points  A,  B,  C , and  D in  the  ground  plane 
may  therefore  he  found  by  erecting  perpendiculars  upon  S0P0  in  a0,  (30,  y0,  and  60.  The  intersec- 


tions of  these  with  the  radials  S„a0,  Sab0,  S0ct>,  and  S0d0  will  locate  the  positions  of  the  points  A,  B , 
C,  and  I)  on  the  platting  sheet. 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


649 


This  construction  is  also  preferably  made  on  a separate  sheet  of  paper.  The  radials  80a0,  S0b0, 
S0c0 , and  S0d0,  fig.  22,  are  drawn  through  their  corresponding  points  on  the  platted  picture  trace 
(or  ground  line)  0o0,/,  and  the  rest  of  the  construction  (fig.  23)  is  made  by  regarding  the  paper 
surface  as  the  principal  plane.  The  designations  are  the  same  as  in  fig.  20.  The  points  d,  /i,  a, 


and  y,  fig.  23,  on  the  line  PPQ  (principal  line)  represent  the  projections  of  the  pictured  points  a,  b, 
c,  and  d in  the  principal  plane;  hence,  their  positions  are  found  by  transferring  the  ordinates  of 
the  pictured  points  to  PPQ  from  P0 : 

P0  S = dd0 ; P0  (i  = bba  ■ Pa  a = aa(t,  and  P„  y = ccQ 

The  radials  from  S through  6,  (3,  a , and  y locate  the  points  d0,  aQ,  and  yc  on  the  line  GG  (or 
S0Po),  fig-  23. 

By  transferring  the  distances  $0d0,  80/30,  SQa0,  and  S0y0,  fig.  23,  to  the  line  80P0  from  <S'„,  tig. 
22,  and  drawing  lines  through  dc,  /3OJ  aQ,  and  y0  parallel  with  0o0o\  their  intersections  with  the 
corresponding  radials  S0d0,  S0b0 , 80a0 , S0c0  will  locate  the  platted  positions  of  the  points  Z>,  B,  A, 
and  C of  the  lake. 

IX.  TO  DRAW  A PLANE  FIGURE  ON  THE  GROUND  PLAN,  BY  MEANS  OF  THE  SO-CALLED 
“METHOD  OF  SQUARES,”  IF  ITS  PERSPECTIVE  AND  THE  ELEMENTS  (POINT  OF  VIEW 
AND  DISTANCE  LINE)  OF  THE  VERTICAL  PICTURE  PLANE  ARE  GIVEN. 

If  we  imagine  the  figure  covered  with  a net  of  squares,  one  set  of  its  sides  being  parallel  with 


Fig.  24- 


0- -^oF 

and  the  other  set  being  perpendicular  to  the  ground  line,  such  net  may  be  utilized  to  draw  the 
outline  of  the  figure  upon  the  ground  plan,  it  being  only  necessary  to  cover  the  pictured  figure 


650 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


a bed  with  the  perspective  of  the  selected  net  in  the  ground  plane,  i.  e.,  the  lines  forming  the 
squares  of  the  perspective  must  have  the  proper  relation  to  the  principal  ray  and  horizon  line. 

The  simplest  disposition  of  the  lines  (forming  the  auxiliary  network)  for  locating  the  figure  is 
the  one  mentioned  above  (parallel  with  and  perpendicular  to  0o0o '),  but  any  other  selection  may 
be  made.  The  squares  may  be  of  equal  size  or  not,  and  the  directions  of  the  lines  composing  the 
network  may  be  given  any  direction. 

In  fig.  24,  in  illustration  of  this  method,  the  lines  in  the  perspective  which  correspond  to  the 


Fig. 25 

sides  of  the  rectangles  that  are  perpendicular  to  the  ground  line  0o0o'  will  vanish  in  the  principal 
point  P,  and  those  parallel  with  the  ground  line  0o0J  will  be  parallel  with  the  horizon  line  00'. 
Selecting  the  lines  of  this  network  so  that  two  lines  of  each  system  will  pass  through  one  of  the 


characteristic  points  of  the  figure  abed , the  perspective  of  this  net  will  appear  as  shown  in  fig.  24, 
where  OJ),  ' represents  the  ground  line  of  the  picture  plane  MN. 

If  we  now  plat  the  principal  plane  S80P0P , fig.  25,  retaining  the  same  designations  as  for  fig. 
20,  the  points  d0,  /?0,  «0,  and  y0  will  represent  (in  the  ground  plane)  the  intersections,  with  the 
horizontal  projection  of  the  principal  ray  8P  (=  80P0),  of  those  net  lines  that  had  been  drawn 
through  P,  P,  A,  and  C parallel  with  the  ground  line. 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


651 


After  platting  the  picture  trace  0o0o ' (of  the  perspective  MN,  fig.  24)  in  the  ground  plane  by 

means  of  the  radials  S0a0,  S0b0 , the  distances  8060,  S080 (fig.  25)  laid 

off  upon  S0P0,  fig.  26,  will  locate  those  net  lines  (parallel  with  0„00')  in  the  ground  plane  which 
correspond  to  the  lines  dS,  bfi  ...  . shown  in  the  perspective  MN,  fig.  24. 

If  we  now  transfer  the  points  aj,  P„,  5,/,  d0',  and  cj  from  lig.  24  to  a strip  of  paper,  and  place 
this  upon  the  picture  trace  0o0o',  fig.  26,  that  the  points  P0  will  coincide,  the  lines  aJA , 50'P,  . . . 

drawu  parallel  with  S0PU  will  represent  the  net  lines  which  are  perpendicular  to  the  ground 
line  0o0'o. 

Thus  the  platted  positions  of  the  points  A,  P,  (7,  and  D are  located  on  the  ground  plane  by 
the  intersections  of  the  corresponding  net  lines  of  both  systems,  as  shown  in  fig.  26. 

The  points  A,  B,  C,  and  J)  will,  of  course,  also  be  bisected  by  the  radials  SQa0,  . . . . , 

which  fact  may  make  it  more  advantageous  to  select  some  other  disposition  of  the  net  lines  for  a 
figure  of  a different  shape. 

When  the  figure  has  a sinuous  perimeter  the  squares  of  the  network  should  be  selected  of  a 
size  sufficiently  small  to  enable  the  draughtsman  to  draw  the  perimeter  sections  falling  within 
the  squares  sufficiently  accurate  to  obtain  a correct  representation  of  the  general  outline. 


We  had  seen,  lig.  26,  that  the  radials  drawn  from  the  so-called  “foot  of  the  station”  ( S0 ) rep- 
resent the  directions  to  the  points  A,  B,  G . . . . in  the  ground  plane,  and  if  we  could 
determine  the  distances  S0A,  80B  ....  (from  the  foot  of  the  station  S0  to  the  points  to  be 

platted  A,  P, ) from  the  perspective  in  some  manner  the  location  of  the  platted 

positions  in  the  ground  plane  would  become  an  easy  matter. 

The  distances  P0A,  80B , fig.  26,  may  be  determined  from  the  perspective  by 

means  of  the  so-called  vanishing  scale,  which  may  be  constructed  as  follows,  fig.  27 : 


MN  = trace  of  picture  plane  in  the  principal  plane,  HE  = trace  of  horizon  plane  in  the 
principal  plane,  GO  = trace  of  ground  plane  in  the  principal  plane,  SS0  = elevation  of  the  station 
8 above  the  ground  plane  GG,  or  above  the  foot  of  the  station  S0. 

A scale  of  equal  parts  is  laid  oft  upon  GO,  to  either  side  of  P„,  and  radials  are  drawn  from  8 
tluough  the  graduation  points  of  the  scale;  their  intersections  with  MN  form  the  vanishing  scale, 
which  may  serve  to  locate  distances  from  the  foot  of  the  station  to  points  to  be  platted  in  the 
ground  plane. 


X.  THE  VANISHING  SCALE. 


N 


652 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


The  picture  trace  0o0o\  fig.  28,  may  have  been  platted  and  the  radials  S0ao , 80b0 , ....  may 
have  been  drawn  on  the  working  sheet. 

It  is  desired  to  locate  the  position  of  a point,  A,  in  the  ground  plane  by  means  of  the  vanishing- 
scale  and  the  picture  a , fig.  29,  of  the  point  A. 

Take  the  ordinate  aa0  from  the  perspective  MX,  fig.  29  (vertical  distance  of  a above  the 
ground  line  0o0u'),  and  lay  it  off  upon  the  vanishing  scale  (fig.  27),  PP0  from  P0  = P0x. 


Fig. 29 


The  line  a. v,  fig.  29,  parallel  with  the  horizon  line  OO1  and  passing  through  a in  the  perspective, 
corresponds  with  the  line  AX,  fig.  28,  parallel  with  the  ground  line  and  passing  through  A in  the 
ground  plane. 

Hence,  if  we  lay  off  80X,  fig.  27,  upon  S0Po  from  80,  fig.  28,  the  point  A (in  the  ground  plane) 
will  be  situated  upon  the  line  XA , iig.  28,  drawn  through  X and  parallel  with  the  ground  line 
00OJ.  The  intersection  of  the  radial  80a0  with  this  line  XX,  fig.  28,  will  be  the  point  A. 


CHAPTER  II. 


PHOTOGRAPHS  ON  INCLINED  PLATES. 

In  the  preceding  we  have  regarded  photographic  plates  (perspectives)  only  that  had  been 
exposed  in  a vertical  plane,  and  although  the  use  of  inclined  plates  for  phototopographic  purposes 
is  not  to  be  generally  recommended  (on  account  of  the  complications  that  will  arise  in  the  ordinarily 
simple  constructions  in  iconometric  platting  from  vertically  exposed  plates,  and  because  the 
relations  which  exist  between  the  elements  of  the  perspective  and  the  orthogonal  projection  in 
horizontal  plan  of  the.  pictured  objects  will  not  be  so  readily  recognized),  still,  occasions  may  arise 
where  the  selection  of  the  available  or  accessible  stations  will  be  so  circumscribed  that  the 
exposure  of  inclined  plates  will  become  necessary  in  order  to  control  the  inaccessible  terrene 
(above  or  below  the  camera  station). 

Photographs  may  also  have  been  obtained  with  au  ordinary  camera,  without  any  device  for 
adjusting  the  plate  in  vertical  plane,  or  the  use  for  iconometric  platting  of  the  photographs 
(perhaps  taken  only  for  illustrative  purposes)  may  have  been  an  afterthought. 

With  reference  to  tig.  (SO  we  have: 

PP  = principal  plane. 

HH  - horizontal  plane  passing  through  the  second  nodal  point  of  the  camera  lens 
(at  the  station  S). 

GG  = ground  plane. 

MN  = picture  plane. 

O'P  = trace  of  picture  plane  MN,  in  the  horizon  plane  HH. 

0\Po  — ground  line  of  picture  plane  MN. 

S0  — foot  of  the  station  8. 

P'P„  = principal  line  of  the  picture  plane. 

P'  = principal  point  of  the  perspective  MN. 

8S„  = vertical  of  the  station;  it  will  penetrate  the  picture  plane  MN  above  (or 
below)  the  horizon  line  at  s.  The  trace  s of  this  vertical  s80  in  the  picture 
plane  is  the  vanishing  point  for  the  perspectives  of  all  vertical  lines  that 
may  be  pictured  on  MN. 

P'SP  = PsS  = a = angle  of  inclination  of  the  plate  MN. 

SP  = (horizontal)  line  from  8 perpendicular  to  horizon  line  O'P. 

8A  = line  of  direction  from  8 to  a point  A , pictured  in  MN  as  a. 

If  we  revolve  SP , in  the  vertical  plane  PP,  about  P until  SP  falls  within  the  picture  plane, 
then  the  point  8 will  fall  into  (8)  and  the  line  8a  will  fall  into  ( S)a . 

The  vertical  plane  containing  the  line  SA  and  passing  through  88„  will  intersect  the  ground 
plane  in  80a0.  If  we  now  revolve  the  line  SnP0,  in  the  vertical  plane  PP,  about  P0  until  S0P„  falls 
within  the  picture  plane  MN,  then  the  point  S0  will  fall  into  ( 80 ) and  the  trace  80an  will  have 
assumed  the  position  ( 80)a0 , and  the  intersection  A of  the  trace  S0a0  with  the  line  of  direction  8a 
will  locate  the  platted  position  of  the  pictured  point  a in  the  ground  plane  GG. 

The  line  sa  intersects  the  ground  line  in  a„ , and  S0a,0  will  be  the  radial  in  the  ground  plane  to 
the  platted  position  of  A and  passing  through  the  foot  8„  of  the  station  S. 

To  find  A on  80a0  we  first  locate  in  the  picture  plane  the  intersection  (A)  of  the  revolved  lines 
( 8)a  and  ( S„)a0 . This  point  (A)  revolved  in  the  vertical  plane  a080S  about  aQ  will  locate  A upon$0a„. 

To  locate  the  position  of  A in  GG,  in  the  manner  just  shown,  we  should  know  the  position  of 
the  line  O'P , as  well  as  the  points  8 and  P.  These  are  kuown  or  may  readily  be  found  if  the 
position  of  the  principal  point  P' , the  length  of  the  distance  line  SP' , and  the  value  of  the  angle 
of  inclination  (cr)  for  the  plate  are  kuown. 


653 


654 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


When  a photographic  plate  in  a surveying  camera  is  intentionally  exposed  in  an  inclined 
position,  it  will  generally  be  exposed  in  such  a way  that  the  principal  line  ff  still  coincides  with 
the  intersection  of  the  picture  plane  MN  and  the  principal  plane  PP,  fig.  30. 

When  the  angle  of  inclination  a is  an  angle  of  elevation  (depression)  the  horizon  line  (inter- 
section of  horizon  plane  and  inclined  picture  plane)  will  fall  below  (above)  the  line  representing 
the  horizon  line  on  the  plate  when  exposed  vertically.  In  order  to  use  the  inclined  plate  for 


iconometric  purposes  the  angle  of  inclination  should  be  observed  directly  iu  the  field,  and,  if  the 
constant  focal  length  of  the  camera  (=/)  is  known,  the  line  SP , fig.  30,  may  be  found  as  the 
hypothenuse  of  the  right-angle  triangle  with  angle  = a and  adjoining  side  =/. 

I.  TO  PLAT  THE  PICTURE  TRACE  OF  AN  INCLINED  PLATE. 

In  order  to  plat  the  picture  trace  the  horizontal  angle,  included  between  the  optical  axis  of 
the  inclined  camera  and  the  horizontal  direction  to  some  known  point,  should  be  measured. 
Should  the  length  SS1  (elevation  of  station  *S'  above  the  foot  of  the  station,  fig.  32),  the  position  of 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


655 


the  line  connecting  two  camera  stations,  and  also  the  position  of  a third  point  A (visible  from 
both  stations)  be  known,  no  horizontal  angle  a needs  to  be  measured  instrumentally,  provided 
the  plates  containing  the  picture  a of  the  third  point  A are  oriented  in  such  a way  that  the  picture 
a be  bisected  by  the  vertical  thread  or  principal  line  ff'  of  the  perspective. 

With  reference  to  lag.  31  we  have 


S'  = platted  position  of  the  station  $ 

S' SL'  = platted  length  and  direction  of  the  base  line. 

The  horizontal  angle  a (at  S')  included  between  this  line  of  direction  S' Si'  and  the  principal 
plane  (or  horizontal  projection  of  optical  axis  S'P0)  may  have  been  observed  in  the  held.  The  line 
S' Sin  fig.  32  represents  the  elevation  of  the  station  S (laid  off  in  the  platting  scale).  If  we  revolve 
this  line  S'S  about  S'PQ  into  the  platting  plane  it  will  assume  the  position  shown  as  S'(S)  in  fig. 
31.  After  erecting  at  (S)  aline  ( S)(P ) perpendicular  to  S'(S)  the  angle  of  inclination  y of  the 
plate  MN  is  laid  off  upon  (S)(P)  from  ( S ). 

(S)(P')  is  made  equal  to  the  constant  focal  length  (=/)  of  the  camera,  and  the  line  drawn 
perpendicular  to  ( S)  (P')  through  [P')  will  represent  the  principal  line  (/)(/')  of  the  perspective  MN, 
revolved  about  S'P„  into  the  platting  plane.  The  point  of  intersection  (s)  of  (S)S'  with  (/)(/') 
represents  the  vanishing  point  for  all  vertical  lines  shown  on  the  picture. 

The  point  of  intersection  P0  of  the  line  (/)(/')  and  the  horizontal  projection  of  the  optical 
axis  S'P„  will  be  the  trace  in  the  ground  plane  of  the  inclined  principal  line  Jf'. 

The  line  P0g,  perpendicular  to  S' P„  in  P0,  is  the  ground  line  or  the  trace  of  the  inclined  picture 
plane  MN  in  the  platting  plane  GG. 


656 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


II.  PLATTING  THE  LINES  OF  DIRECTION  TO  POINTS  PICTURED  ON  AN  INCLINED  PHOTOGRAPHIC 

PLATE. 

The  inclined  picture  plane  MN,  fig.  32,  is  revolved  about  P(tg  into  the  drawing  or  ground  plane, 
when  the  picture  will  appear  as  the  principal  point  P falling  upon  S'P0  = (/)(/')  in  (P) 

and  (P)P0  = PP„. 

To  plat  the  direction  to  a point  A from  S',  we  first  locate  the  orthogonal  projection  a„  (in  the 
ground  plane)  of  the  pictured  point  a,  fig.  31. 

The  image  point  a , fig.  32,  projected  upon  ff  or  upon  PPQ=  a and  a circle  described  about 


P„  with  P0  (a)  will  locate  the  position  (a)  of  the  projected  point  on  the  principal  line  (/)(/')» 
revolved  into  the  platting  or  ground  plane. 

The  perpendicular  to  S'P„  in  a0  and  the  vertical  to  the  ground  plane  OG  from  a,  fig.  32 
intersect  each  other  in  a0,  and  S'a0,  fig.  31,  is  the  horizontal  projection  (in  the  ground  or  platting 
plane)  of  the  line  of  direction  or  radial  from  S'  to  the  point  A. 

III.  DETERMINATION  OF  THE  ALTITUDES  OF  POINTS  PICTURED  ON  INCLINED  PLATES 

We  refer  again  to  fig.  32.  It  is  desired  to  find  the  elevation  H of  the  point  A (pictured  in  a) 
above  the  ground  plane  GO. 

Projecting  a upon  the  principal  plane  PP  we  find  a on  ff ; the  vertical  through  a intersects 
the  horizontal  projection  of  the  principal  ray  S'P0  in  a„,  fig.  32;  hence,  aa0  represents  the  elevation 
• if  the  point  A above  GG , measured  m the  platting  scale. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


657 


With  reference  to  fig.  31,  this  elevation  aa0  (fig.  32)  of  a above  the  ground  plane  is  found  by 
projecting  a upon  P'P0  ( = a in  fig.  32);  the  corresponding  point  on  the  principal  line  revolved 
about  P0  into  the  platting  plane  is  (a)  and  its  orthogonal  projection  upon  the  principal  plane, 
the  latter  revolved  into  the  platting  plane  about  S'P0,  fig.  31,  is  (a);  hence,  the  elevation  of  A 
above  the  ground  plane  is  = («)  a0  = h , to  be  measured  in  the  platting  scale. 

If  2)  = distance  of  the  platted  point  from  S',  taken  from  the  platting  sheet,  E ==  elevation  of 

K 


Fi G.  35. 


the  point  A above  the  ground  plane  GG,  h = (a)  aQ  = aa0,  fig.  32,  = (o)  a0,  fig.  31,  = aan , fig.  33 
S'a0  = d (fig.  31),  taken  from  the  platting  sheet,  the  elevation  H of  the  point  A may  be  found  either 
graphically  from  a diagram,  fig.  33,  or  it  may  be  computed  from  the  relation: 


IV.  APPLICATION  OF  PROFESSOR  HAUCK’S  METHOD. 

The  constructions  just  described  for  locating  the  horizontal  directions  to  points  photographed 
on  inclined  plates  may  be  greatly  simplified  by  applying  Professor  Hauck’s  method,  by  utilizing 
the  properties  of  the  “kernel  points”  of  two  photographs  obtained  from  different  stations  but 
comprising  the  same  ground. 

With  reference  to  fig.  34:  8 and  S1  = the  two  camera  stations. 

Sn  and  80'  = the  foot  points  of  8 and  8'  respectively. 

MN  and  M’N’  = inclined  picture  planes;  both  contain  the  image  a and  a'  of  a point  A 
and  the  pictures  s'  and  s ( “kernel  points”)  of  the  stations  S'  and  8. 
a0  and  a0'  = orthogonal  projections  (in  the  ground  plane  GG)  of  a and  a1 
respectively. 

A0  = orthogonal  projection  of  A in  the  ground  plane. 

2,  s1  and  tt  = kernel  points  for  picture  plane  AIN. 

2',  s and  n'  — kernel  points  for  picture  plane  M'N'. 

These  “kernel  points”  are  of  importance,  inasmuch  as — 

The  horizontal  direction  S0A0  (or  S0'A0)  intersects  the  ground  line  (j(j'  of  MN  (or  M'N')  in  (or 
a'o).  The  line  connecting  a and  s'  (“kernel  point”)  in  7172V7  and  the  connection  of  a'  and  s in  M'N' 
intersect  each  other  in  the  same  point  .Q  of  the  line  of  intersection  of  the  two  picture  planes,  and 
also  intersect  the  ground  lines  gg'  of  the  picture  planes  in  the  “kernel  points”  n and  n ',  respec- 
tively. All  lines  in  TOT,  connecting  s'  with  pictured  points,  and  those  in  M'N1,  connecting  s with 
the  pictures  in  M'N'  of  the  same  points,  intersect  each  other  in  points  £1  of  the  line  of  intersection 
of  the  two  inclined  picture  planes.  The  kernel  points  2 and  2‘  are  the  intersections  of  the 
verticals  passing  through  the  camera  stations  ( 8 and  S'),  with  the  inclined  picture  planes.  They 
are  the  “vanishing  points”  for  the  pictures  of  all  vertical  lines  shown  on  the  negatives,  and  when- 
ever the  pictures  contain  images  of  vertical  lines  the  intersections  of  these  would  locate  2 and 
6584 42 


658 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


2'  on  MN  and  M'N',  respectively.  Still,  when  the  picture  plane  is  inclined  in  such  a way  that 
the  principal  line  of  the  same  would  coincide  with  that  of  the  vertically  exposed  plate  (when  the 
former  were  revolved  about  a line  as  axis  passing  through  the  second  nodal  point  and  parallel 


with  the  horizon  line  00 ' or  HE1,  fig.  34)  the  kernel  point  2 may  more  readily  be  located  upon 
Jf',  as  previously  shown  for  s in  tig.  32. 

In  order  to  locate  the  position  of  Aa,  tig.  34,  with  reference  to  a on  MN  and  a'  on  M'N'  we 
connect  a and  2 and  also  a1  with  2',  which  lines  locate  a0  and  aa'  upon  the  ground  lines  of  the 
picture  planes  MN  and  M'N'.  The  intersection  of  the  lines  S0a0  and  Sja0'  will  give  the  position 
of  A0  in  the  ground  plane  GO. 


CHAPTER  III. 


PHOTOTOPOGRAPHIC  METHODS. 


I.  ANALYTICAL  OR  ARITHMETICAL  METHODS. 


(1)  Method  of  Prof.  W.  Jordan. — In  1874  Professor  Jordan  made  a map  of  tbe  oasis  u Dae  li  el,7 
including  the  village  “Gassr-Dachel,”  based  on  photographs  taken  with  an  ordinary  camera  by 
Remele,  obtained  on  Gerhard  Rohlf’s  African  expedition  during  the  winter  of  1873-74.  Care  was 
exercised  to  expose  the  plates  in  vertical  plane,  and  horizontal  directions  to  at  least  three  points 
for  each  photograph  were  instrumentally  measured  to  obtain  the  data  needed  for  the  proper 
orientation  of  the  pictures.  Vertical  angles  to  at  least  two  such  points  (for  every  picture)  were 
also  observed  to  give  the  means  for  locating  the  horizon  lines  of  the  pictures  and  thus  enabling 
the  draftsman  to  deduce  the  elevations  of  other  points  pictured  on 
the  photographs. 

With  reference  to  tig.  35  we  have:  00'  = horizon  line,  ff — 
principal  line,  P = principal  point,  SP  = focal  length  =/,  variable 
for  different  pictures. 

The  ordinates  aa ',  bb',  and  cc1  — y i,  y> , and  y3,  respectively. 

The  abscissae  of  the  three  points  a,  b , and  c be  xu  x2,  and  x3 
respectively. 

The  horizontal  angles  included  between  the  principal  ray  andthe 
horizontal  directions  8a',  Sb and  8c'  — ax,  a2,  and  a3  respectively. 

The  azimuthal  angles  (between  the  meridian  SN  and  the  hor- 
izontal directions  8a1,  Sb1,  and  8c')  — qjx,  cp2 , and  cp3 

Then  a2  — ax  = cp2  — <Pi  = £i  and  a3  — a2  — cp3  — cp2  = f2 

The  elevations  of  the  points  A,  B , and  C above  the  plane  of 
reference  or  above  the  ground  plane  = Ht,  H2,  and  H3 

As  the  photographic  plate  MN  had  been  exposed  in  vertical  plane,  it  will  be  evident  that  for 
the  three  points  a,  b , and  c pictured  on  the  perspective  MN,  fig.  35 — 


or, 


and 


xx  —f  tan  a x2  =f  tan  a2  x3  — f tan  a3 

x%  — X\=  f (tan  a2  — tan  ax)  = f Sm  ^ 

cos  ax  cos  a2 


x3 


x2—f  (tan  a3  — tan  a2)  = f 


sin  (<*3  — a2) 
cos  0-3  cos  a2 


The  values  x2  — xx  and  x3  — x2  may  be  scaled  off'  directly  on  the  photograph,  and  the  values 
for  a2  — ax  and  a3  — a2  may  be  taken  from  the  field  records  of  the  observed  angles. 


Hence  013  may  be  computed  from  the  equation 


x2  — Xi  _ cos  a3  sin  (a2  — «!) 
x3  — x2  cos  ax  sin  (0-3  — a2) 


If  we  substitute  tan  y for 
and  as 


cos  a3 
cos  ax 


1 + tan  y 
1 — tan  y 


= tan  (45°  + y) 


659 


660 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


we  may  now  write 


tan  (45°  + y)  = 


1 + 
1 - 


cos  a3 

cos  _ cos  ay  -f-  cos  a3 
cos  O' 3 cos  «i  — cos  a3 

cos  O, 


cos  a + cos  "3 


a\  4-  a3  . 
sill  — L_ L — ? sin 


= cot  ai  + a3  cot  ^1- 

ax  — a3  2 2 


and  tan  A'1  a'd  - cot  (45°  + y)  cot  013 


From  this  equation  we  compute  ay  + a3,  and  after  subtracting 


from 
we  find 


03  — a2  — <p3  — (p3~  £2 


a3  — ay  = q>i  — cf>\  — 


**1  — cx3  = qjy  — cp3 


knowing  ay  + o3  and  ay  — a3  we  can  readily  find  ay  and  a3,  also, 


fl'2  = ay  + £x  or 


We  had  found: 


— o3  — £2 


x2  - xy  = /®il1  =f slrLfl ; hence  /=^-^)coso,  cos  o2 

cos  ay  cos  a2  cos  a 1 cos  a2  sm  £1 

x,  - x , =/sin  (»■-«■)  =/ Bip  ^ , whence /=  <*»  ~ -r->  003  "»  008  a= 

cos  o3  cos  a2  cos  o3  cos  a2  sin  f2 

Thus  the  abscissae  x2,  and  x3,  (the  principal  lin  eff)  and  the  focal  length  /may  be  found. 

With  the  aid  of  the  observed  vertical  angles  ft  the  horizon  line  OO'  may  be  located  on  the 
photograph.  For  example,  if  the  vertical  angle  ft3  = c 8 & had  been  observed  to  the  point  (7, 
we  find : 

y3  = 8&  tan  ft3 

f 

= tan  ft3 

cos  a3 

The  horizon  line  OO1  will  fall  below  the  pictured  point  c by  the  vertical  distance  — — — tan  ft3, 

COo  ^3 

and  for  the  point  a tlie  vertical  distance  to  the  horizon  line  would  be 


2/i= 


/ 

COS  ay 


tan 


fti 


At  least  two  vertical  angles  having  been  observed  for  each  plate,  the  horizon  line  OO'  may  thus  be 
located  and  marked  upon  the  negative,  when  the  principal  point  P may  also  be  marked  on  OO'  by 
means  of  the  abscissa}  xx,  x2,  and  x3  — a'P , b'P,  and  Pc' , respectively. 

( 2 ) Method  of  Dr.  G.  Le  Bon. — Dr.  Le  Bon,  who  used  his  instrument  chiefly  for  the  draughting 
of  ancient  buildings  and  monuments  in  India,  provided  the  ground-glass  plate  of  his  camera  with 
a net  of  squares,  each  square  having  sides  1 centimeter  long,  the  latter  being  drawn  parallel  with 
the  horizon — and  principal  lines,  which  latter  two  were  subdivided  into  millimeters. 

This  arrangement  enabled  the  operator  to  obtain  the  measurements  of  objects  directly  by 
inspection  of  the  image  on  the  (graduated)  ground-glass  plate.  To  determine  the  dimensions  of 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


661 


the  front  of  a building,  a certain  distance  is  measured  directly  upon  the  same  and  a picture  is 
then  taken  by  exposing  a photographic  plate  in  vertical  plane  and  parallel  to  the  base  of  the  front 
of  the  building. 

For  example : 

(a)  To  find  the  distance  D of  an  object  of  unknown  height  H. 

Two  stations,  S and  S',  are  occupied  on  a base  line  (which  is  measured  directly  in  the  field)  laid 
oft'  in  a direction  at  right  angles  to  the  base  of  the  object,  fig.  36. 


If  the  height  of  the  image,  measured  on  the  graduated  ground  glass,  at  the  first  station  S is  h 
and  the  focal  length  for  both  exposures  be  the  same  =/,  then 

D : II  =f:  h 

and  for  the  second  station  S1 

I)  + B : H = f : h' 

By  dividing  the  second  equation  by  the  first,  we  find: 

I)  + B h B _h  h — Id 

I)  ~ h'  ’ 1)  ~ h‘  -1  ~ h' 

whence : 


B is  given  and  h and  h‘  are  measured  directly  on  the  ground  glass. 

(b)  It  is  desired  to  find  the  height  H of  an  object  of  which  the  fractional  length  I1‘  had  been 
measured  directly,  fig.  37. 


On  the  image  of  the  object  on  the  graduated  ground-glass  plate  the  heights  h and  h'  may  be 
read  oft'  directly,  and  II  being  known  we  find  II  from  the  equation 


(3)  Method  of  L.  P.  Paganini  ( Italian  method). — This  method  was  developed  for  the  topographic 
survey  of  Italy,  made  under  the  auspices  of  the  Boyal  Italian  Military  Geographical  Institute, 
and  a detailed  description  of  the  same,  with  numerical  examples,  has  been  published  in  Appendix 


662 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


No.  3,  Report  for  1893  of  the  Superintendent  of  the  United  States  Coast  and  Geodetic  Survey. 
Also,  Dr.  C.  Koppe  and  Prof.  F.  Steiner  give  preference  to  the  arithmetical  method  for  photo- 
gram metric  surveys  in  general. 

GENERAL  ARITHMETIC  DETERMINATION  OF  THE  ELEMENTS  OF  THE  ITALIAN  PHOTOGRAPHIC  PERSPECTIVES. 

The  panoramic  views  which  subserved  the  map  making  were  obtained  by  ten  successive 
exposures.  After  each  exposure  the  camera  was  moved  in  azimuth  by  a horizontal  angie  of  36°, 

and  as  each  plate  subtends  a horizontal  angle  of  42°, 
the  two  ends  of  adjoining  plates  have  a common  mar- 
gin of  a width  of  3°  in  arc,  corresponding  to  a width 
of  15  millimetres.  These  common  margins  of  two 
adjoining  plates  serve  principally  to  ascertain 
whether  the  adjustments  of  the  phototheodolite  have 
g been  changed  during  the  occupancy  of  a station. 

-y  (a)  Orientation  of  the  picture  trace. — The  hori- 
zontal projection  of  one  complete  panorama  com- 
posed of  ten  plates  will  be  a regular  decagon,  tig.  38, 
with  a radius  of  the  inscribed  circle  equal  to  the 
principal  focal  length  (constant)  of  the  camera. 

P',P2,  ....  p10--  (horizontal)  picture  traces, 

V = panorama  station, 

VP'  = VP2  = ....  UP10  =/=  principal  focal 

length  of  camera. 

After  the  position  of  one  panoramic  view  has  been  platted  on  the  map,  its  picture  trace  will 
be  oriented,  and  with  it  the  remaining  nine  views  of  the  panorama. 

After  the  horizontal  angle  go,  tig.  39,  included  between  the  principal  ray  VP'  of  view  P'  and 
the  horizontal  direction  to  the  triangulation  point  8,  fig.  39,  has  been  platted 
the  orientation  of  each  succeeding  view  P2,  P3  . 
plislied  by  adding  successively  36°,  72°,  108°  . 
the  angle  go. 

( b ) Platting  the  l ines  of  direction  to  p ictured  po  int  s 
of  the  terrene. — The  orientation  of  the  panorama  hav- 
ing been  made,  the  lines  of  direction  to  points  pho- 
tographed on  the  panorama  plates  may  readily  be 
platted. 

The  plate  MN,  fig.  39,  may  represent  a vertical 
photographic  plate  oriented  with  refer- 
ence to  the  known  point  8,  pictured  on  x 

MN  as  s.  s 


00 1 = horizon  line,  « 

V = point  of  view  of  the  perspective 
MN, 

go  - angle  of  orientation  for  this  plate 
with  reference  to  8, 

VP  — f — (principal)  focal  length, 
ss\  perpendicular  to  00'  — y — ordinate 
of  the  image  s , 

sx  perpendicular  to  ff  — x — abscissa  of 
the  point  s. 


Fig.  39 


From  the  rectangular  triangle  VP's',  fig.  39,  we  find  : 


x = / tan  go. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


663 


It'  the  camera  station  V and  tlie  known  point  A have  been  platted  and  the  picture  trace  00', 
fig.  40,  has  been  oriented,  the  horizontal  projection  of  the  ray  from  V to  S may  be  found  as  follows: 


Fig. 4-0 

'""oA 


The  abscissa  P's'  = x,  fig.  39,  is  laid  off  on  00',  fig.  40,  from  P'  in  the  sense  of  the  direction  to 
S (whether  8 is  to  the  right  or  to  the  left  of  the  principal  line  ff,  fig.  39)  with  reference  to  the 
principal  point  P',  locating  s'  (the  orthogonal  projection  of  the  pictured  point  in  the  ground  plane) 
and  a line  drawn  from  V through  s'  = Vs',  which  will  be  the  ray  ThS',  fig.  39,  projected  in  the 
platting  plane. 

The  position  of  8 on  the  platting  sheet  is  obtained  by  finding  the  point  of  intersection  of  two 
or  more  lines  of  direction,  obtained  in  a similar  manner,  from  other  pictures  containing  images  of 
8 and  taken  from  different  stations,  as  all  rays  to  the  same  object,  seen  from  different  stations, 
must  intersect  each  other  in  the  same  point  on  the  platting  sheet. 

The  elevations  of  pictured  terrene  points  are  readily  determined  after  the  selected  points 
(identified  on  several  pictures)  have  been  determined  and  platted  in  horizontal  plane,  in  the 
manner  just  described. 

If  the  elevation  of  the  station  Fis  known,  the  elevation  of  the  line  of  horizon  00'  on  the  plate, 
fig.  39,  may  easily  be  obtained  by  adding  the  height  of  instrument  to  the  elevation  of  I". 

(c)  Determination  of  the  elevations  of  pictured  points. — Disregarding  the  effects  of  curvature 
and  refraction,  the  elevations  of  all  the  points  on  the  plate  which  are  bisected  by  the  horizon  line 
00'  have  the  same  elevation  as  the  optical  axis  of  the  instrument  at  Tr. 

The  elevations  of  pictured  points,  above  or  below  the  horizon  line,  are  obtained  by  determining 
their  elevation  above  or  their  depressions  below  the  line  00' . 

If  D — horizontal  distance  from  station  V to  a point  8,  fig.  39, 

= F$',  fig.  39,  to  be  measured  in  the  platting  scale. 

L = difference  in  elevation  between  point  8 and  station  V. 

= 88'  (S'  being  the  orthogonal  projection  of  8 upon  the  platting  plan). 
d — horizontal  distance  of  the  picture  s of  8 from  V. 

We  find  from  the  similar  triangles  IVs  and  V88': 

L : D - y : d 1 


From  the  rectangular  triangle  VP's ' follows: 


d — — = f sec  oj,  2 a 

COS  CO 


whence 


L = _ IhJ  . 
j sec  go 


o 


664 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


Should  the  point  8 be  bisected  by  the  vertical  thread  (principal  plane)  then 

go  = 0 and  sec  go  — 1 , or, 


This  formula  would  answer  for  all  points  of  the  perspective  if  the  image  plate  were  a cylin- 
drical surface  of  radius  =/ (instead  of  being  a tangential  plane  to  such  cylinder),  if  the  decagon 
were  a circle  (as  it  is  the  case  for  the  sensitive  film  of  the  panoramic  cameras,  and  Colonel 
Moessard’s  cylindrograph,  which  will  be  described  later). 

Differences  of  elevation,  taken  from  the  perspectives,  are  positive  or  negative  according  to 
the  relative  positions  of  the  pictured  points  with  reference  to  the  horizon  line  OO',  fig.  39,  whether 
above  00'  or  below  the  same,  and  the  apparent  elevations  of  such  points  (above  mean  sea  level) 
are  obtained  by  adding  their  ordinates  (L,  fig.  39)  to  or  subtracting  them  from  the  elevation  of  the 
camera  station  ( V,  fig.  39). 

By  comparing  the  elevations  thus  obtained  for  identical  points  from  photographs  exposed  from 
different  stations  the  hypsometric  determinations  of  secondary  points  of  the  terrene  may  be 
checked. 

(d)  Checking  the  position  of  the  horizon  line  of  a photograph. — To  check  the  position  of  the  hori- 
zon line  00',  fig.  39,  photographs  are  selected  which  show  the  images  of  two  or  more  triangnlation 
points,  the  elevations  of  the  latter,  determined  from  the  photographs,  are  compared  with  those 
given  in  the  triangnlation  records  and  discrepancies  are  adjusted  by  shifting  the  line  00'.  Should 
the  elevations  of  the  triangulation  points  be  unknown,  or  should  the  pictures  from  any  station  not 
contain  the  pictures  of  such  points,  this  check  may  still  be  made  by  measuring  the  vertical  angles 
[a,  fig.  39,  with  the  vertical  circle  of  the  phototlieodolite  from  such  camera  station)  to  a series  of 
prominent  points  ( 8 , fig.  39)  and  comparing  their  computed  ordinates  ( L , fig.  39)  with  those 
obtained  from  the  pictures. 

We  find  from  the  similar  triangles  VS  S'  and  1 rss',  fig.  39: 

tan  SVS'  = tan  a — ~ 

1)  d 

and  we  had  according  to  formula  2a: 


hence 


cos  00 


tan  a = % cos  go,  or  4 

/ 

/'.  tan  a r 

V = - 5 

COS  GO 

where  go  is  the  horizontal  angle  included  between  the  vertical  plane  ( VS  S')  passing  through  the 
camera  station  V and  the  point  8,  fig.  39,  and  the  principal  plane  ( Vff ).  This  angle  go  should 
be  measured  (with  the  horizontal  circle  of  the  phototheodolite)  for  several  points  S at  every  sta- 
tion, whence  a limited  or  insufficient  number  of  triangnlation  points  may  be  seen. 

If  the  computed  values  for  y,  formula  5,  are  not  in  accord  with  those  obtained  by  direct 

measurement  on  the  photograph,  the  horizon  line  00' , fig.  39,  must  be  adjusted  until  the  values 

for  the  ordinates  measured  on  the  picture  are  tin*  same  as  those  computed  by  aid  of  formula  5. 

The  necessity  of  the  precise  determination  of  the  value  / (focal  length)  is  evident  from  the 
preceding,  and  if  the  panorama  pictures  contain  a sufficient  number  of  well-defined  pictures  of 
surrounding  triangulation  points,  the  determination  of  / may  readily  be  made  by  means  of  the 
adjusted  horizon  line  00',  fig.  39. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


665 


(e)  Determination  of  the  focal  length  /.—The  phototheodolite  is  set  up  over  a well-determined 
point  and  adjusted.  A plate  is  exposed  in  vertical  plane  in  such  a way  that  the  vertical  thread 
ff  bisects  a known  geodetic  point  S , fig.  41,  which  can  readily  be  identified  upon  the  ground-glass 
plate  of  the  camera.  (It  is  also  desirable  that  the  ordinate  y,  fig.  41,  be  sufficiently  long  to  assure 
a correct  measurement  of  its  length  to  be  made  on  the  picture.)  There  will  be  given,  fig.  41: 


S 


L = difference, of  elevation  of  bisected  point  S and  panorama  station  V,  D = horizontal  dis- 
tance between  8 and  V,  y = ordinate  of  pictured  point  s. 

From  equation  3 a we  find 


/ = 


D.y 

L 


which  will  be  a fairly  accurate  value  if  the  horizontal  position  of  the  camera  was  assured  and  if 
the  ordinate  y was  correctly  measured  on  the  negative. 

Another  value  for / may  be  found  from  equation  5: 


/= 


y.  cos  oo 
tan  a 


if  the  picture  contained  triangulation  points  enough  to  adjust  the  horizon  line  by  computing  their 
ordinates: 

L .d 


By  using  the  mean  of  these  determinations  for /the  computations  (based  upon  the  new  values  for 
x and  y)  may  be  repeated  until  perfect  agreement  is  reached. 

(/)  Determination  of  the  principal  point  of  the  perspective. — The  great  number  of  triangulation 
points  established  in  Italy,  with  special  reference  to  the  phototopographic  survey,  facilitates  the 
application  of  the  photogrammetric  method  and  assures  the  accurate  determination  of  the  per- 
spective elements.  Although  the  Italian  pictures  command  a horizontal  angle  of  but  12°,  the 
greater  number  of  them  contain  the  pictures  of  several  triangulation  points,  and  it  can  be 
ascertained  simultaneously  with  the  determination  of  the  value  of  / whether  the  picture  P,  of  the 


666 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


intersection  of  the  cross  wires  (00'  and  ff)  coincides  with  the  principal  point  of  view,  P,  upon 
the  perspective,  fig.  42. 

s and  s'  = pictures  of  two  triangulation  points  S and  S'  on  the  photograph  MN,  V = station 
point  or  point  of  view;  ss  and  s's'  = y and  y'  respectively  = verticals  upon  the  horizon  line  00' 
through  the  picture  points  s and  s',  = ordinates  of  the  triangulation  points;  SSt  and  S' Si'  = L aud 
L'  respectively,  = differences  in  elevation  between  the  triangulatiou  points  and  camera  statiou; 
D and  I)‘  — horizontal  distances  from  V to  S and  S'  respectively ; x and  x'  = abscisste  of  pictured 


S 


points  s and  s';  d and  d'  = horizontal  distances  of  the  pictured  triangulation  points  from  the  point 
of  view  V. 

It  is  desired  to  find  VP  and  the  position  of  P with  reference  to  s and  s',  or  the  abscissae 
x and  x'. 

L,  L',  D,  D ',  y,  and  y'  are  known,  or  they  may  be  found  by  direct  measurements  on  the  chart 
projection  and  upon  the  photograph.  Hence: 


The  horizontal  angle  sTs'  ( = oo  + &/)  being  observed  in  the  field  the  other  two  angles,  y and 
6,  of  the  horizontal  triangle  sTs',  may  be  computed  as  follows: 


tan 


d'  — d 
d + d' 


cot 


s Vs' 


By  substituting  H for  ^ ^ and  M for  = 90"  — 

2t  £ 


we  will  find 


y = M + N 
6 = M - N 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


667 


From  tlie  two  triaugles  sVP  and  PVs'  (both  are  rectangular  at  P)  we  find 

f=d.  sin  y = d'  sin  6 
x = /.  cot  y 
x‘  = /.  cot  S 

also,  as  a check,  the  angles  of  orientation : 

go  — 90°  — y 
go 1 = 90°  - 6 


To  check  the  absciss*  the  length  ss1  is  carefully  measured  upon  the  negative,  which  length 
should  equal  the  computed  value  of 


x + x'  and  also  = 


(d  + d1)  sin 


sTV 


cos 


6 — y 


Should  the  horizontal  angle  sFs'  not  have  been  measured  in  the  field  for  some  reason,  then  the 
angles  y and  6 may  be  found  by  computation,  after  carefully  measuring  ss ' on  the  negative  and 
using  the  formulas 


where: 


tan 


tan  {I 


l(P  - d')  (p -ss')  and 

V p (p  - d) 

l(p  - d)  (p-  ss') 

V p{p  - d') 


d + d'  + ss1 
P = 9 


the  angles  of  elevation  a and  which  are  obtained  either  by  direct  measurement  in  the  field  or 
computed  from  the  formulas 


tan  a = 


tan  a‘  — 


D 

TJ 

D' 


serve  to  obtain  checks  on  the  values,  measured  on  the  negatives,  for  y and  y1  by  using  the  formulas 

y = — f—  tan  a and 
cos  GO 


y‘  - 


— P — - tan  a' 
cos  go' 


the  value  for  / in  above  formulas  being  the  same  as  found  from  the  equation 


/ = d.  sin  y = d'.  sin  6 


By  repeating  the  computation  with  these  values  for  y and  y'  (if  any  discrepancy  is  noted 
between  these  new  and  the  former  values  for  y and  y')  the  true  value  for  / may  be  obtained  very 
closely. 

For  all  practical  purposes,  however,  it  suffices  to  take  several  pictures  with  a constant  focal 
length,  and  to  take  the  mean  value  of  the  different  / determined  from  those  pictures. 


668 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


/ 


s . 

-o 


P M 
0—0 


0' 


\\ 

\ ' 
\ 

\ 


\R 


m 


-4 O, 


\ 


\ 


\ 


A \ 


7 


{(j)  Franz  HafferVs  method  for  finding  the  focal  length  of  a photograph  from  the  abscissce  of  two 
pictured  triangulation  points. — When  the  horizontal  distances  T)  and  1)'  are  great,  compared  with 

the  differences  in  elevation  ( L and  L')  between  the 
points  in  question  (S  and  S')  and  the  camera  station 
V,  fig.  42,  the  ordinates  y and  y ' will  be  short,  their 
lengths  will  be  difficult  to  be  measured,  and  it  may 
\ be  better  in  that  case  to  determine  the  value  for 
\ / by  means  of  the  abscissm  of  the  pictured  points, 

/ \ fig.  43. 

/ ( 00'  = platted  (and  oriented)  picture  trace,  Vs  and 

Vs'  = platted  horizontal  directions  from  the  camera 
station  V to  the  triangulation  points  S and  8'  (pictured 
/ i as  s and  s'),  YP  = perpendicular  to  the  picture  trace 

/ through  V. 

/ It  is  desired  to  find  /. 

/ Describe  a circle  through  the  three  points  V,  s and 

s',  the  center  of  which  may  be  at  0. 

The  angle  sCs ' = 2 (sIV).  The  perpendicular 
'"•d—  — " through  C to  ss'  (=  CM)  will  bisect  this  line  and  the 

Fig.  4-3  center  angle  sCs1  into  two  equal  parts;  hence,  sCM 

and  s'  CM  each  = s Vs',  and  if  the  radius  of  the  cir- 
cle passing  through  s,  s'  and  V = B we  will  have  the  following  relation  (from  the  triangle  sMC): 


Yc 


R/  I 


-/- 


/ 


/ 


/ 


/ 


/ 


/ 


sC  — B = 


sM 

sin  s CM  ‘ 


x + x‘ 

9 


sin  sCM ’ 


„ , x + x‘ 

sM=  77- 


Haviug  drawn  the  diameter  mn  parallel  with  00',  we  will  have 

f=  VP  = VA  + AP 


VA  being  vertical  to  mn  it  will  be  the  middle  proportional  to  mA  and  An: 


mA  :47=17  : An  or 
mA  • An  — A V2 

JqI  __  'JQ 

We  can  now  replace  mA  by  (mC  — AC)  = B — : — ^ — 
and  as 

An  = nC  + AC  = B + ^7^ 


we  find: 


and  finally: 


17  = 


AP  = CM  = SM  cot  MCs 


x'  + X 


cot  sCM 


(4)  General  arithmetical  method  for  finding  the  platted  positions  of  points  pictured  on  photographic 
perspectives  ( exposed  in  vertical  plane). — If  we  refer  the  pictured  points  to  the  principal  point  /'  by 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


669 


means  of  tlie  rectangular  system  of  coordinates  formed  by  the  principal  line  ff  and  the  horizon 
line  00'  we  will  have  with  reference  to  fig.  44: 

8 and  S'  = two  camera  stations;  MN  and  M'  N'  = two  picture  planes  exposed  in  vertical 
plane,  one  from  station  S,  the  other  from  station  81 ; aa'  ( = y)  and  a'  P ( = x)  = coordinates  of 
pictured  point  a on  MN-,  a'  a\  (=  y1)  and  a\  P'  (=  x')  = coordinates  of  a'  pictured  on  M'  N'  -, 
f = focal  length  (the  same  for  both  pictures  MN  and  M ' N')-,  D = S0A0  = horizontal  distance  of 
A from  station  8 ; D'  — S'0A0  = horizontal  distance  of  A from  station  S' ; d = Sa'  = 80a0  = hor- 
izontal distance  of  pictured  point  a from  point  of  view  d‘  — S'<X\  = S0'a0'  = horizontal  distance 
of  pictured  point  a'  from  point  of  view  S'-,  R=  elevation  of  A above  horizon  plane  of  station  8. 
H'  = elevation  of  A above  horizon  plane  of  station  S';  B = S0S0'  = horizontal  distance  between 
the  stations  S and  and  a‘  = horizontal  angles  included  between  B and  the  principal  planes 
passing  through  S and  S',  respectively. 

If  the  camera  (theodolite)  was  in  perfect  .adjustment,  if  the  base  line  B is  known,  and  if  the 


A FigAV  * 


angles  a and  a'  had  been  observed,  we  will  know  the  values  of  B,  a,  «',/,  and  the  coordinates 
x , y , x' , and  y' , the  latter  being  obtained  by  direct  measurement  on  the  negatives. 

We  can  now  compute — 

(1)  The  horizontal  angle  y,  included  between  the  principal  plane  and  any  horizontal  direction, 
Sa',  fig.  44,  from  the  equation : 

x x' 

tan  y = j or  tan  y'  = .. 


(2)  The  angle  of  elevation  ft  of  the  line  of  direction  Sa  to  any  point,  A,  pictured  as  a on 
the  photograph  MN. , from  the  equation : 

V v' 

tan  ft  — ^ or  tan  ft'  = 

As 

d = Vp  -f  x1  or  d'  = V f1  [x'Y 

we  may  also  write : 


or 


tan  ft  — 
tan  ft'  = 


-1= 

V P -f-  x2 

y' 

V/2  + ( x'f 


670 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


We  know  the  length  SoS0'  (=  B)  of  the  triangle  80A0S0',  and  the  angles  y,  a,  y‘  and  a1  also  being 
given,  we  have 

D:B  — sin  (y1  +«') : sin  [180°  — (y  + a r + y‘-\-  a')] 
sin  (y1  + a') 
sin  (y  + a + y'  -|-  «') 


or 


80A0  = D = 


B sin  ( y‘  + a' ) 
sin  (y  + a -f-  y'  + oc') 


S0'A0  = D' 


B sin  (y  + a) 
sin  (y  + a + y‘  4-  a1) 


The  difference  in  elevation,  if,  between  the  point  A and  camera  station  8 may  be  found  from 


— tan  fi 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


671 


whence 

or 


H — I)  tan  /i 
IV  = D'  tan  /i. 


(?)  General  arithmetical  method  for  finding  the  platted  positions  of  points  pictured  on  photographic 
perspectives  for  inclined  picture  planes. — For  inclined  picture  planes  we  will  have  to  take  into 
consideration  the  angle  of  inclination  of  the  plate— the  angle  which  is  included  between  the 
optical  axis  of  the  inclined  camera  and  the  horizon  plane  of  the  camera  station. 

We  have,  with  reference  to  tigs.  45  and  40: 


a = horizontal  angle  between  the  principal  plane  of  station  8 and  the  vertical  plane  passing 
through  station  8 and  the  point  A,  pictured  as  a on  inclined  picture  MN;  — angle  of  elevation 
of  the  point  A observed  from  8;  y = angle  of  inclination  of  the  photographic  plate  MN ; 6 = 
180°  — y;  00'  = horizon  line  on  MN  when  vertical,  permanently  marked  on  the  camera;  P = prin- 
cipal point  for  the  vertical  plate,  also  permanently  marked  as  the  intersection  of  the  principal 


672 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


and  horizon  lines  when  the  plate  is  vertical;  Pn  = y = ordinate  of  a on  MW  (fig.  46);  an  = x — 
abscissa  of  a on  JOT,  very  nearly  = a'P';  2 = vanishing  point  (“kernel  point”)  for  all  vertical 
lines  pictured  on  MW. 

From  inspection  of  fig.  46  it  will  follow  directly: 


and 


, aa' nn‘ STI 

tan  SW'  - - sfd 

Pp  — PIJ  _ y cos  y — / sin  y 
~ Vp  + (Sn')2~VP^{Sn+  nn'f 
y cos  y — f sin  y 
V x 2 + (iS'/I  -f  pn)1 
_ y cos  y — / sin  y 
V x 2 + (/cos  y + y sin  y)1 

a'n'  x x 

tan  a = . = -=7= = ; 

tin1  iSU  + pn  / cos  y + y sm  y 


(We  had  found  for  the  vertically  exposed  plate 


tan  (3  = 


tan  a — 


and 


The  preceding  formulas  for  tan  a and  tan  ft  will  assume  the  form  of  the  latter  if  the  angle  of 
inclination  y is  reduced  to  zero,  as  sin  y — sin  0 = 0 and  cos  y = cos  0 = 1.) 

After  having  thus  found  a and  ft  (also  a'  and  ft')  we  can  now  compute  the  value  for  D = $0A0 
and  for  H = AA' 

With  reference  to  fig.  45  we  have 

sin  (s'  — a') 


D 

B~ 

hence 

D = 

and  from 

tan  ft  = 

we  find 

B sin  [180°  — («+  t -4- 1‘ — «')] 

B sin  (f7  — a') 
sin  {a  + e + e'  — a') 

R 


H = D tan  ft  * 

B (y  cos  y —/sin  y) 

V afl  + (/cos  y + y sin  yf 

If  an  ordinary  surveying  camera,  with  a constant  focal  length,  is 
used,  and  when  it  should  become  desirable  to  expose  a photographic 
plate  in  an  inclined  plane,  the  complement  6 of  the  augle  of  inclina- 
tion of  the  optical  axis  (=  y)  may  be  determined  more  readily  (but 
only  approximately)  than  the  latter  by  carefully  measuring  the  dis- 
tances AD,  fig.  47  (in  the  direction  of  the  line  of  a suspended  plumb 
bob),  and  DB , supposing  AB  to  be  parallel  with  the  photographic 
plate. 

(6)  General  analytical  determination  of  the  elements  of  a photo- 
graphic perspective. — If,  in  addition  to  the  photographs,  data  obtained 
by  instrumental  observations  are  given  for  a graphical  determination 
of  the  focal  lengths  of  the  pictures,  their  horizon  lines  and  principal  points,  then  these  elements 
may  also  be  determined  by  computation. 

A picture,  MW,  may  contain  the  images  a,  h,  and  c of  three  known  points,  A,  B,  and  C,  the 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


673 


position  of  the  camera  station  (whence  this  picture  was  obtained)  being  likewise  known  with 
reference  to  the  three  platted  points  A ',  B',  and  C',  fig.  48. 

To  orient  the  picture  trace  (or  ground  line)  gg'  with  reference  to  the  platted  station  S',  and 
the  platted  points  A',  B',  and  C',  the  latter  are  preferably  referred  to  a system  of  coordinates 
having  the  platted  station  S'  as  origin. 

In  tig.  48,  for  example,  a rectangular  system  of  coordinates,  S'Y  and  S'X,  has  been  adopted, 
with  the  origin  in  S',  and  axis  of  abscissa  passing  through  one  of  the  three  triangulation  points. 

The  coordinates  of  the  three  triangulation  points  A‘ , B1,  and  C',  platted  on  the  chart  projection, 
are  found  by  measurement  = X1Y1,  X2Y2,  and  X3,  respectively. 

The  coordinates  of  the  orthogonal  projections  (on  the  picture  trace  gg')  of  the  corresponding 
points,  pictured  on  the  photograph  MX,  may  be  designated  by  xgy,,  xuyu , and  xul , respectively. 


The  horizontal  distances  between  a and  b,  b and  c,  a and  c (which  are  the  same  as  those 
between  a'  and  b',  b'  and  c',  a'  and  c'  on  the  picture  trace)  may  be  m\  m",  and  mlu,  respectively. 
We  will  find  directly,  from  an  inspection  of  fig.  48: 

(1)  yv  : x,  = Y1  : X! 

(2)  y,i  : xu  = 1 2 • X2 

(3)  yl  : = mm  : m11 

(4)  \xm  — x ,)  : (xn  — xx)  = mm  : m1 

(5)  (xm  - x ,)2  + y,2  = (m111)8 

From  these  five  equations  the  five  unknown  quantities  x„  y„  xn,  yu,  and  xm — the  coordinates 
of  the  points  a',  b',  and  c',  which  ore  to  be  located — may  be  computed. 

From  the  area  of  the  triangle  S'a'c ' 

.'/>•  _ /• 

O — o 

jLJ  £ 

we  find  the  focal  length 

/• 2/i  • 'rm 

/ - ^ mlll 


6584 43 


674 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


The  horizontal  angle  of  orientation  y — included  between  the  principal  ray  S'P'  and  the 
horizontal  direction  to  C (=  S'C') — may  be  found  from  the  equation: 


cos  y = -z 

X 


f 


or  = % 
mr 


The  principal  point  P'  may  now  be  located  upon  gg1  from  c'  by  making 

P'&  = xm  sin  y. 

The  differences  in  elevation  between  the  camera  station  S and  the  three  triangulation  points 
A,  _7>,  and  G being  known,  it  will  now  be  an  easy  matter  to  draw  the  horizon  line  upon  the 
photograph  and  mark  the  position  of  the  principal  point  P on  the  same. 


II.  GRAPHICAL  ICONOMETRIC  METHODS. 

(1)  Method  of  Col.  A.  Laussedat. — Colonel  Laussedat’s  methods  of  constructing  topographic 
maps  from  perspective  views  of  the  terrene,  having  been  widely  published,  form  the  groundwork 
for  all  subsequent  work  in  this  direction;  they  are  chiefly  of  a graphical  character  and  they  are 
in  harmony  with  the  laws  of  perspective. 

Laussedat  considers  two  cases  in  reconnaissance  surveys  for  geographic  expeditions  to 
which  photo-topographic  methods  may  be  applied  with  advantage: 

(1)  The  explorer  may  remain  sufficiently  long  in  one  locality  to  make  a survey  on  a large 
scale,  say  1 :20  000,  and  even  larger  for  special  purposes. 

(2)  The  explorer  moves  rapidly  from  place  to  place,  gathering  only  the  most  necessary  data 
on  his  itinerary  to  enable  him  to  plat  the  topography  of  the  traversed  country  as  a “running- 
survey  ” on  a small  scale — say  1:50  000  and  even  smaller — preserving  and  representing  only  the 
principal  topographic  features  met  with  on  the  track  survey. 

In  the  first  mentioned  case  the  explorer  will  measure  one  or  more  base  lines,  with  as  great  an 
accuracy  as  the  means  at  hand  and  the  time  at  his  disposal  will  admit.  He  will  then  cover  the 
area  to  be  mapped  with  a system  of  triangles,  connected  with  (or  founded  upon)  the  base  line, 
and,  inasmuch  as  the  triangulation  stations  will  be  occupied  with  the  surveying  camera,  the 
scheme  should  be  laid  out  with  due  reference  to  the  subsequent  iconometric  platting  of  the 
topographic  features. 

When  applying  the  ordinary  surveying  methods  the  triangulation  scheme  would  probably  be 
laid  out  with  a view  toward  covering  as  large  a territory  as  possible,  occupying  the  least  number 
of  intervisible  points.  With  the  use  of  photography,  however,  the  conditions  are  changed;  every 
topographic  feature  that  is  to  be  platted  iconometrically  should  be  seen  from  two  or  more  camera 
stations.  The  latter  are  to  be  triangulation  stations,  or  they  will  have  to  be  tied  on  to  the  general 
scheme  by  special  supplementary  instrumental  observations.  Still  it  is  not  always  essential  that 
the  highest  peaks,  which  maybe  included  in  the  trigonometric  survey  (as  concluded  points),  should 
also  be  occupied  with  the  camera,  as  frequently  other  camera  stations  will  answer  the  requirements 
just  as  well. 

Regarding  the  second  case,  where  the  explorer  follows  a certain  route,  making  only  the  most 
necessary  (and  at  best  but  short)  side  excursions,  the  photo-topographic  method  is  even  of  greater 
value  than  in  the  first  case,  particularly  when  traversing  open  and  broken  country.  For  this 
kind  of  reconnoissance  it  may  be  well  claimed  that  the  photographic  method  surpasses  all  other 
surveying  methods  regarding  the  amount  of  data  which  maybe  collected  in  a limited  time  period. 

All  topographic  operations  and  instruments  serve  to  measure  vertical  and  horizontal  angles, 
and  a photographic  perspective  (of  which  the  focal  length  and  the  positions  of  the  horizon  line 
and  principal  point  are  known)  will  give  all  the  data  needed  to  determine  the  vertical  and  hori- 
zontal angles  of  lines  of  direction  drawn  from  the  point  of  view  to  all  points  pictured  on  the 
photograph. 

The  points  A and  7>,  pictured  ou  the  vertical  plate  MN,  lig.  49,  may  represent  the  images  of 
two  distant  mountain  peaks;  a and  h will  be  their  orthogonal  projections  upon  the  horizon  line 
HH‘  (picture  trace  in  horizontal  plane  11R). 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


675 


a S b = a = horizontal  angle  between  lines  of  direction  from  the  station  to  the  two  peaks,  A 
and  B.  SP  (perpendicular  to  HH')  — distance  line  or  focal  length  of  the  picture  MN. 

The  vertical  angles  ft  and  y may  be  shown,  in  horizontal  plan,  by  revolving  the  vertical 


planes  passing  through  8 A and  SB  about  the  lines  8a  and  8b,  respectively,  until  they  coincide 
with  the  horizon  plane  RE.  This  has  been  done  in  hg.  49  for  the  vertical  plane  8 a A: 

a A = a (A)  and  (A)  a 8 = A a 8=  90° 

A S ft  = ( A ) S ft  = ft. 

The  vertical  angles  ft  and  y may  now  be  measured  in  horizontal  plan  as  {ft)  and  (y). 

To  indicate  the  general  method  of  iconometric  platting,  and  to  show  how  the  platted  features 
of  the  terrene  may  be  obtained  from  the  photographs,  we  will  refer  to  figs.  50  and  51. 


FlG. 50 


A,  7»,  and  0 are  three  camera  stations,  platted  in  horizontal  plan,  whence  three  perspectives, 
I,  II,  and  III,  fig.  51,  of  the  same  knoll  D were  obtained.  The  traces  of  these  three  pictures  on 
the  platting  sheet,  fig.  50,  may  be  I ft  Aa , Er  H ;,  H Hr.  All  three  photographs  may  have  been 
obtained  with  the  same  camera  of  constant  focal  length— the  distance  lines  PA  A,  PB  B , and  Pc  C 
are  of  equal  length. 


676 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


(a)  Locating  points  identified  on  several  photographs  on  the  platting  sheet. — The  three  stations  A, 
B , and  G are  platted,  either  as  parts  of  the  triangulation  system,  or  by  measuring  the  base  line  AB 
on  the  ground  and  measuring  the  horizontal  angles  CAB , GBA,  and  ACB,  after  which  the  sides 
AG  and  BG  may  be  found  graphically  (or  by  computation)  and  the  triangle  ABC  may  now  be 


I I 31 


platted  upon  the  working  plan.  Horizontal  angles  or  directions  to  D having  also  been  observed 
from  A,  B,  and  C,  its  position  with  reference  to  those  three  points  may  also  be  platted.  To  plat 
the  three  picture  traces  HH  we  must  know  the  horizontal  angles  PAd  (=  a),  which  are  observed 
in  the  field  for  each  picture  by  means  of  the  horizontal  circle  attached  to  the  phototheodolite. 


The  angles  a are  platted  as  aA 


and  a'c,  fig.  50,  and 


O-— 

\ 


(A) 


the  constant  focal  length  (=/)  of  the  three  negatives  I, 
II,  and  III,  fig.  51,  is  laid  oft’  on  the  radials  iPA,  PPB,  and 


F|  G.  52 


CP, 

Pr 


l 


/ 


c.  Perpendiculars  erected  to  these  lines  in  PA,  PB,  and 
c,  respectively,  will  represent  the  oriented  picture  traces 
PA/P,  HJI B,  and  ECHC,  when  the  absciss*  PAdA,  PBdB,  and 
Pcdc,  measured  on  the  negatives  I,  II,  and  III,  should  equal 
the  lengths  PAdA , Pvdu,  and  Pcdc  on  the  picture  traces. 

The  point  I)  is  termed  a “ reference  point.”  Every 
picture  that  is  to  be  used  in  iconometric  platting  should 
contain  the  image  of  at  least  one  such  reference  point  of 
known  position  in  both  the  horizontal  and  vertical  sense. 

After  the  picture  traces  HH  have  once  been  platted, 
any  other  point,  P,  of  the  terrene,  shown  on  two  or  more 
photographs,  may  readily  be  platted  from  the  photographs 
without  requiring  instrumental  measurements  in  the  field. 

To  locate  the  platted  position  of  the  point  T,  shown 
on  two  pictures,  I and  III,  as  t,  the  abscissae,  PAtA  and  Pctc, 
are  laid  off  on  the  picture  traces  HAHA  and  HCHC,  respec- 
tively, from  PA  and  Pc  and  on. the  proper  side  of  P to  corre- 
spond with  the  position  of  the  image  t with  reference  to  the 
principal  point,  P,  of  the  perspectives.  Lines  drawn  from  A 
and  G through  tA  and  tc,  fig. 50,  represent  the  lines  of  hori- 
zontal directions  to  T,  and  their  point  of  intersection  locates 
the  position  of  T on  the  plat  with  reference  to  A , B , and  C. 

(h)  Determination  of  the  elevations  of  pictured  points. — 
The  horizon  line  HIP  of  a perspective,  fig.  49,  being  the 
intersection  of  the  vertical  picture  plane  MN  with  the  horizon  plane  (passing  through  the  optical 
axis  of  the  camera),  will  intersect,  points  in  the  picture  which  in  nature  have  the  same  elevation 
as  the  optical  axis  of  the  camera  or  as  the  point  of  view  8. 


'6 


REPORT  FOR  1897 PART  IT.  APPENDIX  NO.  10. 


677 


The  distances  Sa  and  SA,  fig.  52,  are  measured  on  the  platting  sheet  and  the  ordinate  aA , 
fig.  49,  of  the  pictured  point  a,  on  the  negative.  Perpendiculars  are  then  erected  to  8A  in  A and  a 
and  the  latter  is  made  equal  to  the  ordinate  of  a taken  from  the  picture  — A a — a (a),  fig.  52.  If  we 
now  draw  the  line  8(a)  (to  its  intersection  with  the  perpendicular  in  A),  then  the  triangles  8a  (a) 
and  SA  (A)  will  be  similar  and  the  angle  AS  (A)  will  represent  the  vertical  angle  (of  elevation)  of 
the  visual  ray  from  S to  A revolved  about  /SA  into  the  plane  of  the  horizon  or  into  the  platting 
plan.  Prom  the  similar  triangles  Sa  (a)  and  SA  (A)  we  derive  the  proportional  equation: 

A (A) : 8A  = a (a) : 8a 

whence 


A (A)  = 


a (a) . /SA 


sa 


The  value  found  for  A (A)  measured  on  the  platting  scale  will  give  the  difference  in  elevation 
between  camera  station  horizon  and  the  point  A. 

In  practical  work  the  elevations  of  the  camera  stations  are  known,  and  by  adding  the  height 
of  the  instrument  including  the  value  A (A)  to  the  elevation  of  *S,  fig.  49,  the  absolute  height  of 
A will  be  found,  wdiich,  however,  is  still  to  be  corrected  for  curvature  and  refraction. 

A second  value  for  the  elevation  of  A maybe  found  in  the  same  manner  for  another  negative 
containing  the  image  a (taken  from  another  station),  and  the  mean  of  several  such  determinations 
is  adopted  for  the  final  value  for  the  height  of  A. 

( c ) Drawing  the  plan,  including  horizontal  contours. — After  some  little  practice  points,  pictured 
on  different  negatives  but  representing  identical  points  in  nature,  will  readily  be  identified  by  the 
observer  and  he  will  soon  be  able  to  pick  out  the  characteristic  points  to  reproduce  the  water 
courses,  watersheds,  roads,  canals,  etc.,  on  the  platting  sheet.  After  these  principal  guide  lines 
have  been  well  located  on  the  chart,  buildings,  outlines  of  woods,  marshes,  etc.,  are  platted, 
including  everything  that  is  to  be  shown  on  the  finished  map. 

Enough  points  should  be  platted  iconometrically  to  give  a good  control  for  a correct  delinea- 
tion of  the  relief.  When  the  number  of  points  determined  on  the  plan  is  sufficient,  or  if  they  are 
favorably  located  to  give  an  adequate  control  only  for  the  delineation  in  the  horizontal  sense, 
additional  points  should  be  platted  in  order  to  obtain  an  equally  good  control  of  the  terrene  in  the 
vertical  sense. 

The  planimetric  work  completed,  elevations  of  as  many  of  the  platted  points  as  seem  neces- 
sary (or  additional  ones)  are  determined  and  inscribed  on  the  chart.  Horizontal  and  equidistant 
contours  may  now  be  drawn,  by  interpolation,  to  harmonize  with  the  elevations  suffixed  on  the 
chart  to  the  points  of  control,  conforming  their  courses  (between  the  located  points)  to  the 
configuration  of  the  terrene,  as  it  is  shown  on  the  photographs. 

It  can  not  be  denied  that  a certain  amount  of  study  and  practical  application  are  required  to 
enable  the  draftsman  to  correctly  interpret  forms  of  the  terrene,  shown  in  perspective.  Yet, 
it  should  also  be  admitted  that  such  translation  or  conversion  of  the  relief  of  the  terrene  into  the 
horizontal  map  projections  may  be  far  more  accurately  accomplished  (at  one’s  leisure)  by  means 
of  geometrically  correct  perspectives,  than  could  be  accomplished  by  sketching  in  the  field. 
When  topographic  features  are  sketched,  as  seen  from  one  direction,  they  will  frequently  be  found 
to  have  been  misconceived  when  they  are  seen  again  from  another  (not  anticipated)  point  of  view. 
Of  course,  the  platted  forms  may  then  be  corrected  in  a measure,  at  least,  still,  many  details  are 
sketched  which  will  not  be  .seen  again  from  other  stations,  and,  even  those  that  are  seen  again 
under  other  conditions  may  not  be  modified  to  conform  to  their  true  shapes,  unless  the  original 
station,  whence  they  were  first  seen  and  sketched,  could  be  reoccupied  to  verify  the  suggested 
changes  and  corrections.  Generally  speaking,  topographers  regard  a second  occupation  of  a 
station  with  little  favor,  it  being  considered  too  great  a waste  of  time,  retarding  progress,  and 
considerably  increasing  the  cost  of  the  work. 

In  iconometric  platting,  however,  it  is  always  an  easy  matter  to  refer  back  again  to  panoramic 
views  obtained  from  some  other  station,  and  the  platting  of  topographic  details  should  not  be 
attempted  without  having  first  made  a careful  study  of  and  a close  comparison  between  the 
various  pictures  representing  the  same  features  but  seen  from  different  points  of  view. 

(2)  Method  of  Dr.  A.  Meydenbaur. — The  pantoscopic  lens  (made  by  E.  Bush,  Bathenow, 


678 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


Prussia)  of  Dr.  Meydenbaur’s  surveying  camera  commands  an  angle  of  about  100°.  By  excluding 
an  external  ring  of  the  effective  disk  of  these  lenses  by  means  of  a diaphragm,  pictures  are 
obtained  subtending  an  angle  of  but  06°,  requiring  six  plates  for  a complete  panorama. 

This  camera  has  neither  telescope  nor  vertical  circle  but  it  is  provided  with  a horizontal  circle, 
thus  enabling  the  operator  to  control  the  revolutions  of  the  camera  in  azimuth. 

After  this  camera  has  been  set  up  and  adjusted  over  a station  the  panorama  is  photographed 
by  exposing  six  plates  in  succession,  each  successive  turn  in  azimuth  of  the  camera  covering  an 
angle  of  60°,  fig.  53,  and  two  adjoining  plates  lapping  over  each  other  by  3°  in  arc.  These  com- 
mon margins  (like  Paganini’s  plates)  contain  identical 
sections  of  the  panorama  view.  They  may  serve  to  find 
the  value  for  the  focal  length  of  the  pictures,  and  they 
control  the  permanency  of  the  camera’s  adjustments  dur- 
ing one  complete  revolution  in  azimuth. 

(a)  Determination  of  the  focal  length  for  the  pano- 
rama views. — From  the  six  plates,  covering  the  entire 
horizon  from  one  station,  objects  may  be  selected  on  the 
center  lines  of  the  common  margins  of  adjoining  plates 
which  should  be  equidistant  from  the  principal  lines  of 
the  two  plates. 

After  having  selected  a series  of  such  reciprocal 
points  (using  a magnifying  glass  if  necessary)  on  all  six 
plates,  we  will  have  obtained  twelve  determinations, 
represented  by  the  length  l,  for  the  position  of  the  prin- 
cipal line.  The  greatest  discrepancy  between  any  two 
values  should  not  exceed  02  mm,  if  the  instrument  was 
well  adjusted.  The  sum  =21  of  two  such  distances 
(between  two  of  the  corrected  principal  lines)  will  rep- 
resent the  effective  lengths  of  one  picture,  or  the  length  of  one  side  of  a regular  hexagon,  with 
an  inscribed  circle  of  the  radius  equal  to  the  constant  focal  lengths  (=/)  of  the  negatives. 

This  length  =/may  be  found  graphically  or  it  may  be  computed  from  the  formula: 

l 

J tan  30° 

When  positive  prints  are  to  be  used  in  the  iconometric  map  construction  it  will  become  neces- 
sary to  correct  this  focal  length  / to  correspond  with  any  changes  that  may  have  taken  place  in 
the  dimensions  of  the  prints  when  compared  with  their  negatives.  By  comparing  the  distances 
between  the  “ teeth  ” (marking  the  principal  and  horizon  lines)  on  the  negative  with  those  included 
between  their  contact  prints  on  the  positive  the 
total  linear  changes  of  the  print  in  the  directions  of 
the  principal  and  horizon  lines  are  readily  found. 

We  have  with  reference  to  fig.  54:  ah  -----  original 
length  included  between  the  teeth  marking  the  hori- 
zon line  on  the  negative,  a'h'  = length  of  horizon 
line  (included  between  the  pictured  teeth)  on  the 
positive  print,  co  = f = constant  focal  length  of 
camera  or  negative. 

If  we  draw  the  triangle  ahO , place  the  line  a'h' 

(measured  on  the  print)  parallel  with  ah  and  move  the  same  (maintaining  its  direction  parallel 
with  ah)  toward  (or  from)  0 until  a'  falls  upon  ao  and  b'  upon  ho , then  c'O  will  be  the  local  length 
of  the  photograph  (‘‘contracted,”  in  our  case).  This  determination  of  f should  be  made  for  every 
print  that  is  to  be  used  in  the  iconometric  map  construction. 

The  topographic  map  is  graphically  constructed  from  the  negatives  and  prints  in  a manner 
very  similar  to  that  described  for  Colonel  Laussedat’s  method. 

( h ) General  method  of  iconometric  platting. — With  reference  to  fig.  55  we  have: 

I and  II  — two  negatives  of  plates  exposed  from  camera  stations  I and  II,  respectively. 
I II  = baseline,  measured  in  the  field. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


679 


The  elevations  of  camera  stations  I and  II  may  be  known  and  negative  I may  contain  the 
image  of  station  II,  negative  II  that  of  station  I.  After  the  baseline  I II  has  been  platted  in 
reduced  scale  (in  the  scale  of  the  proposed  map),  circles  are  described  about  I and  II  as  centers 


with  radii  = cO  = f—  constant  focal  length  of  the  negatives.  Then  make 

I IIr,  = Oil , (PI.  I)  and 
II I0  = OI„  (PL  II). 

Describe  arcs  from  II0  with  II„c  = x'u  (plate  I)  and  from  J0  with  l0c  = x'\  (PI.  II)  as  radii, 
transpose  ct0  = x\  (PI.  I)  on  the  tangent  II0c  and  ct0  = x'\  (PI.  II)  on  the  tangent  I„c. 


680 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


The  prolongations  of  t0I  and  t'0I  will  be  tangential  directions  to  the  sides  of  the  tower  T 
(pictured  on  Pis.  I and  II)  from  camera  station  I,  and  <0II  and  U0II  will  be  the  tangential  direc- 
tions to  the  sides  of  the  same  tower  T from  station  II.  These  four  tangents  intersect  each  other 
at  T in  a quadrangle,  the' inscribed  circle  of  which  will  represent  the  position  of  the  tower  (in 
horizontal  plan)  with  reference  to  the  baseline  I II. 

Any  other  points,  common  to  both  Pis.  I and  II , may  be  located  in  horizontal  plan  in  pre- 


cisely the  same  manner.  The  method  just  described  is  general  in  character,  but  when  the  camera 
is  provided  with  a-  horizontal  circle,  enabling  the  observer  to  cover  the  horizon  with  six  plates  by 
revolving  the  camera  exactly  <J0°  in  azimuth  after  each  exposure,  the  following  method  is  generally 
applied : 

The  constant  focal  length  = /of  the  negatives  is  laid  off  on  the  principal  line  below  the 
principal  point  — c'O  for  negative  I and  = c"0  for  negative  II.  The  images  ot  the  stations  are 
projected  upon  the  horizon  lines,  Sn  upon  77,  J/,  (Plate  I)  and  *Sj  upon  HnHn  (PI.  II)  when 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


681 


d 08„  = a'  represents  the  horizontal  angle  included  between  the  principal  plane  and  base  line 

I II,  and  c"OS,  = a"  represents  the  corresponding  horizontal  angle  for  station  II.  These  angles 
a'  and  a"  are  transferred  from  the  negatives  I and  II  to  the  corresponding  ends  of  the  base  line 
I II,  as  indicated  in  iig.  5G. 

After  laying  off  the  focal  length  / from  the  base  stations  I and  II  upon  the  sides  of  the  angles 
a'  and  a"  ( = Id  and  lie"  respectively)  and  erecting  perpendiculars  ( H'll  and  H"H")  in  & and  o'' 
to  Ic'  and  lie"  respectively,  they  will  represent  the  oriented  picture  traces  of  negatives  I and  II. 

The  remaining  two  sets,  of  live  plates  each,  of  the  panorama  views  at  the  stations  I and  II, 
are  easily  oriented  and  platted,  the  next  plate  in 
order  at  station  I,  for  instance,  will  have  the 
optical  axis  in  the  direction  a ' + 00°,  the  third : 
a'  + 120°,  etc. 

After  all  the  horizontal  projections  of  the  ver- 
tical plates  (picture  traces)  11,11,.  HiH^  .... 
i/i76,  tig.  57,  have  been  platted  at  both  stations  I 
and  II,  the  horizontal  projections  of  all  points  that 
may  be  identified  on  two  plates  are  marked  and 
platted  by  locating  the  intersections  of  the  lines  of 
direction  drawn  through  the  projections  on  the 
picture  traces  of  the  pictured  points  in  the  same 
manner  as  shown  in  fig.  56  for  the  tower  T.  Every 
platted  camera  station  will  be  surrounded  by  a 
regular  hexagon  formed  by  the  picture  traces  of 
the  six  plates  comprising  the  panorama  set. 

(c)  Determination  of  the  elevations  of  pictured 
points  of  the  terrene. — The  projection  in  horizontal 
plan  of  an  object  having  been  platted,  the  eleva- 
tion 1(8,)  of  that  object  8,  above  (or  the  depression 
of  it  below)  the  horizon,  HIT,  of  the  camera  station 

II  may  be  found  as  follows : 

The  lengths  118, ( = OS,  on  PI.  II)  and  I II,  fig. 

56,  may  be  measured  on  the  platting  sheet,  and  the 
ordinate  ys  may  be  taken  from  the  negative  II. 

We  erect  perpendiculars  to  I II  in  8,  = ya  = 8,  (S,)  and  in  I,  then  draw  the  line  II(S,)  to  its 
intersection  (8,)  with  the  perpendicular  to  I II  in  I,  when  the  length  /(S', ),  measured  in  the 
platting  scale,  will  represent  the  difference  in  elevation  between  the  points  I and  11. 

By  computation  we  would  find  from : 


\ Ft  G 57 


\ 


1(8,)  : ya  = I II : 8,  II 


A 8,)  = */s 


III 
8]  II 


If 


the  scale  of  the  map  is 


1 

M 


we  will  have: 


/( 8, ) = M.ys 


III 

8,11 


The  values  of  ys , I 71,  and  8,11  are  found  by  direct  measurements  with  a small  ivory  scale 
divided  into  0-5  mm.,  of  which  0-1  mm.  may  be  estimated  after  a little  practice. 

(3)  Method  of  Capt.  E.  Deville  ( Canadian  method).— This  so-called  Canadian  method  has  been 
in  use  under  the  auspices  ol  the  department  of  the  interior  of  the  Dominion  of  Canada  since  1888. 
Deville  has  given  a full  account  of  these  methods  in  Photographic  Surveying,  published  at  the 
government  printing  bureau,  at  Ottawa,  in  1895,  and  the  following  paragraphs  have  been  largely 
taken  from  Deville’s  book  : 

(a)  General  remarks  on  field  ivorlc. — The  area  to  be  surveyed  is  covered  with  a triangulation 
net,  preferably  before  the  phototopographic  survey  is  commenced,  and  a secondary  triangulation  is 


682 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


carried  along  with  the  phototopographic  work  to  locate  the  camera  stations  in  both  the  horizontal 
and  vertical  sense,  with  reference  to  the  primary  triangulation  stations  already  established. 

The  surveyor  makes  a rough  plat  of  the  entire  triangulation  (in  the  field),  on  which  he  locates 
all  the  stations  occupied  to  enable  him  to  recognize  the  weak  points  of  his  work  and  to  plan  his 
operations  with  a thorough  understanding  and  good  assurance  of  success.  The  instrumental 
work  in  the  field  is  done  merely  to  locate  the  camera  stations  and  certain  reference  points  (if  the 
triangulation  points  are  not  sufficiently  close  together),  all  topographic  features  being  deduced 
from  the  pictures. 

The  camera  stations  are  located  either  by  angles  taken  from  the  station  to  surrounding 
triangulation  points,  by  resecting,  or  by  angles  observed  from  the  latter  to  the  signal  left  over  the 
camera  station,  by  intersecting,  or  by  both  methods  combined. 

The  final  value  of  the  work  depends  in  a great  measure  upon  a judicious  selection  of  the 
camera  stations  in  order  to  bring  the  relief  of  the  entire  terrene  under  proper  control  and  to  be 
enabled  to  plot  all  points  needed  for  a full  development  of  the  terreue  by  the  method  of  intersec- 
tions of  horizontal  liues  of  direction. 

Other  methods  for  platting  the  topographic  features  and  details  are  employed  only  when  the 
method  of  intersections  fails  on  account  of  the  camera  stations  not  being  well  situated,  or  on 
account  of  an  insufficiency  of  data  to  give  the  requisite  number  of  horizontal  lines  of  direction 
for  a good  location  of  points  by  “intersecting.” 

Each  camera  station  should  be  marked  by  a signal  of  some  kind  before  leaving  it,  not  to  be 
shown  on  the  pictures,  but  to  be  observed  upon  with  the  transit  or  altazimuth  from  other  stations 
in  order  to  locate  the  correct  position  of  the  camera  station  on  the  platting  or  working  plan. 

Frequently  it  will  be  of  advantage  to  set  the  camera  up  excentrically  over  a tri angulation 
station  in  order  to  include  certain  additional  parts  of  the  landscape  in  the  views.  The  position 
of  the  excentric  camera  station,  with  reference  to  the  triangulation  point,  can  readily  be  ascer- 
tained, and  should  always  be  carefully  recorded. 

Complete  panorama  sets  are  not  taken  at  every  camera  station,  it  being  preferred,  rather,  to 
increase  the  number  of  stations,  often  occupying  a station  to  obtain  a single  view  only,  if  by 
doing  so  better  intersections  for  the  icouometric  location  on  the  platting  sheet  of  some  special 
feature  are  obtained.  Multiplicity  of  stations  demands  but  a small  increase  in  labor,  either  in 
the  field,  in  the  extra  observations  of  directions  to  reference  points  for  their  location,  or  in  the 
iconometric  platting  in  the  office,  and  enough  stations  should  always  be  occupied  to  give  a full 
control  of  the  relief  of  the  area  to  be  surveyed. 

A certain  section  of  the  terrene  may  be  so  located  that  it  will  be  a difficult  matter  to  select 
more  than  one  station  whence  it  may  be  seen.  In  such  a case  the  method  of  “vertical  intersec- 
tions” may  often  become  useful:  Two  or  more  views  of  such  area  are  taken  from  stations  at 
different  elevations , the  greater  the  difference  in  altitude  between  such  stations  the  longer  will  the 
base  line  be,  and  the  better  are  the  intersections  which  locate  the  features  in  question,  if  the  latter 
are  not  too  far  away. 

As  enough  plates  should  be  exposed  to  cover  the  ground  completely,  the  camera  stations 
Avill  have  to  be  distributed  in  such  a way  that  all  valleys,  sinks,  and  depressions,  that  may  be 
represented  in  the  scale  of  the  map,  are  well  controlled  (i.  e.,  seen  from  different  camera  stations). 
It  is  evident,  therefore,  that  the  number  of  stations  to  be  occupied  for  the  phototopographic 
development  of  a certain  area  will  depend  in  a great  measure  upon  the  character  of  the  terrene 
and  upon  the  scale  of  the  chart. 

Two  or  three  well-defined  points  (so-called  reference  points)  in  each  panorama  view  (covered 
by  one  plate)  are  observed  with  the  transit  or  altazimuth  noting  and  recording  the  vertical  and 
horizontal  angles  upon  the  outline  sketch  made  f >r  every  plate  exposed.  Such  sketches  serve  to 
identify  points  with  far  more  certainty  than  a mere  designation  or  description  of  the  points 
observed  upon.  The  general  triangulation  notes  are  kept  in  the  usual  manner. 

Vertical  angles  are  observed  to  check  the  position  of  the  horizon  line  on  every  photograph 
and  to  correct  errors  due  to  small  changes  in  the  level  adjustments  of  the  camera  that  may  arise 
during  the  transportation  of  the  instrument  over  a rough  trail.  The  horizontal  angles  are  needed 
for  the  location  of  the  camera  stations  and  for  the  orientation  of  the  pictures  (picture  traces)  on 
the  platting  sheet  for  the  subsequent  map  construction. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


683 


(b)  General  remarks  on  the  iconometric  platting  of  the  survey. — The  field  notes  of  the  phototopo- 
grapliic  surveys  made  in  the  Northwest  Territory  of  the  Dominion  of  Canada  by  the  topographical 
surveys  branch  of  the  department  of  the  interior  (under  Capt.  E.  Deville,  surveyor  of  Dominion 
lands),  are  platted  on  a scale  of  1:20000,  but  the  maps  are  published  on  a scale  of  1:40000,  with 
(equidistant)  contours  of  100  feet  vertical  intervals. 

The  phototopographic  reconnaissance  in  southeastern  Alaska,  executed  by  Dominion  land 
surveyors  under  Dr.  W.  F.  King,  Alaskan  boundary  commissioner  to  Her  Majesty,  was  platted 
on  a scale  of  1 : 80000  and  published  on  a scale  of  1: 160000,  with  horizontal  contours  of  250  feet 
vertical  intervals. 

It  is  assumed  that  the  triangulation  computations  have  been  made  and  that  the  triangulation 
points  have  all  been  platted,  and  that  their  elevations  above  the  adopted  reference  plane  have 
been  affixed  to  the  marked  points  on  the  platting  sheet. 

The  triangle  sides  of  the  secondary  triangulation  scheme  (executed  during  the  phototopographic 
survey)  are  now  computed  (the  corrections  to  the  horizontal  angles,  indicated  by  the  closing  errors, 
having  been  applied),  the  latitudes  and  departures  (from  every  secondary  point  to  the  nearest 
primary  station)  are  computed,  and  the  secondary  stations  are  then  platted  by  their  latitudes 
and  departures  (unless  the  primary  triangulation  sides  are  too  long). 

The  camera  stations  (not  included  in  the  secondary  triangulation  scheme)  are  now  platted  with 
reference  to  the  triangulation  points,  using  a table  of  chords  or  a station  pointer  (three  arm  vernier 
protractor).  If  many  points  had  been  observed  upon  from  the  camera  station,  the  horizontal 
angles  are  preferably  laid  off  on  a piece  of  tracing  paper,  and  this  improvised  multi-arm  protractor 
is  used  like  a station  pointer  to  locate  the  station. 

The  surveyor  should  endeavor  to  obtain  at  least  one  direction  from  a triangulation  station  to 
every  camera  station;  the  (iconometric)  platting  will  then  be  less  troublesome  and  more  accurate. 

Photographs  should  not  be  used  for  platting  the  positions  of  camera  stations,  as  this  would 
not  locate  them  with  sufficient  precision,  and  enough  angles  should  always  be  observed  in  the  field 
to  locate  every  occupied  station  in  the  manner  just  mentioned. 

From  the  original  negatives  copies  are  made,  enlarged  to  94  by  13  inches  on  heavy  bromide 
paper,  more  recently,  however,  a special  brand  of  bromide  paper,  known  as  “platino  bromide,” 
has  been  used  by  Captain  Deville.  The  enlargement  adopted  in  Canada  for  these  bromide  prints 
is  about  2.1  times  larger  than  the  negatives,  which  ratio  was  selected  to  utilize  the  full  width  of 
the  paper  found  in  market. 

These  bromide  enlargements  are  used  extensively  in  the  map  construction,  and  they  should  be 
made  with  great  care  to  reduce  distortion  to  a minimum.  Before  using  the  prints  for  the  map 
construction  any  distortion  due  to  the  enlarging  process  should  be  ascertained,  which  is  done  in 
the  following  manner: 


Join  the  middle  notches  II  and  II1,  indicating  the  position  of  the  horizon  line,  and  7'  and  B' 
representing  the  position  of  the  principal  line,  fig.  58,  and  with  a set  square  test  these  two  lines  for 
perpendicularity.  Take  with  a pair  of  dividers  the  distance  between  the  two  notches  A and  B 
(which  on  the  negative  is  equal  to  one-lialf  of  the  constant  focal  length)  and  see  whether  it  is 


684 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


equal  to  the  distance  of  the  corresponding  two  notches  C and  £>.  Now  apply  one  of  the  points 
of  the  dividers  in  P;  the  other  should  come  in  E and  F.  Transfer  the  point  to  P'  and  check  the 
length  P'G  and  P'J  in  the  same  way.  If  the  print  satisfies  all  these  tests,  it  may  be  used  for 
the  iconometric  platting;  if  it  does  not,  it  is  returned  to  the  photographer  with  a request  for  a 
better  one. 

(c)  Platting  the  picture  traces. — Every  photograph  contains  at  least  one,  generally  several,  of 
the  triangulation  points  platted  on  the  working  sheet,  and  the  traces  of  both  the  picture  plane  and 
principal  plane  are  found  and  platted  on  the  plan  as  follows: 


The  distance,  or  principal  line  PS,  fig.  59,  is  made  equal  to  the  focal  length  of  the  picture,  and 
the  image  point  a of  the  point  A is  projected  upon  the  principal  line  (=  a)  and  upon  the  horizon 
line  ( = «').  If  S\  represents  the  platted  position  of  the  camera  station  S on  the  plan,  and  if  SiA, 
represents  the  horizontal  direction  on  the  plan  from  S to  A,  we  make  Stat  — Sa'  (taken  from  the 
photograph)  and  from  au  as  center,  with  a a (=  Pa')  as  radius,  describe  a circle  to  which  Sip  is 
drawn  tangent,  then  Si p — trace  of  principal  plane  and  the  perpendicular  to  Sxp  through  ax  = 
pax  — trace  of  picture  plane. 

Instead  of  making  this  construction  on  the  “photograph  board,”  which  will  be  described 
further  on,  it  can  be  made  on  the  plan  itself,  as  follows: 


On  take  S\B , fig.  60,  equal  to  the  focal  length  of  the  print;  erect  BC  perpendicular  to 
Sx A i in  B and  equal  to  a a,  fig.  59.  Join  S\C  and  take  St p equal  to  the  focal  length;  at  p erect  a 
perpendicular  to  Sx G and  it  will  represent  the  trace  of  the  picture  plane,  while  SXG  is  the  trace  of 
the  principal  plane. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


685 


Another  simple  method,  avoiding  the  drawing  of  constructive  lines  on  the  plan,  is  as  follows: 

Take  a triangle  of  hard  rubber  or  wood  and  mark  oft'  along  one  side 
the  focal  distance  SP,  fig.  50,  of  the  print,  = ab,  fig.  61,  and  carefully 
notch  the  triangle  side  at  b so  that  the  center  of  a fine  needle,  marking 
the  platted  station  point,  will  just  fit  into  the  notch.  From  the  print, 
fig.  59,  take  the  abscissa  of  the  pictured  point  a — aa  = Pa ' between  the 
points  of  a pair  of  dividers,  move  the  triangle,  fig.  61,  about  the  needle 
(which  marks  the  platted  station)  with  the  left  hand  until  ac,  fig.  61,  is 
equal  to  the  distance  aa  held  between  the  points  of  the  dividers.  The 
triangle  is  held  securely  in  this  position  and  lines  are  drawn  along  the 
triangle  sides  ab  and  ac.  Prolong  ac  beyond  a and  check  the  distance  ac 
again  to  be  = aa.  The  line  be  represents  the  horizontal  direction  from 
the  platted  station  b to  the  platted  reference  point  c (on  the  negative, 
fig.  59,  the  picture  of  the  corresponding  reference  point  is  a).  We  will 
now  have:  ba  = trace  of  the  principal  plane,  ac  = trace  of  the  picture 
plane,  a = projection  of  the  principal  point  on  the  platting’  sheet. 

The  trace  of  the  principal  plane  (=  ab)  is  preferably  marked  on  the 
platting  sheet  by  a short  line  only,  bearing  an  arrow  pointing  toward  the 
platted  station  (b)  whence  the  picture  was  taken,  and  the  principal  point 
a is  marked  to  correspond  with  the  designation  of  the  print.  It  may  be 
remarked  here  that  as  few  lines  as  possible  are  drawn  on  the  platting 
sheet  to  avoid  confusion  and  mistakes.  (See  photograph  board.) 

( d ) The  identification  of  pictured  points  on  several  photographs  repre- 
senting identical  points  of  the  terrene. — The  topographic  survey  being 
platted  mainly  by  the  intersections  of  horizontal  directions,  points  con- 
trolling the  relief  of  the  same  area  must  be  identified  on  sets  of  pictures 
taken  from  different  stations.  When  selecting  such  points  on  a photograph  preference  should  be 
given  to  those  which  best  define  the  surface  relief  or  terrene,  like  characteristic  points  of  ridges, 
peaks,  saddles,  changes  of  slope,  changes  in  the  river  courses,  etc.,  each  point  being  marked  by 
a dot  in  red  ink  on  the  photograph  and  having  a number  or  symbol  affixed  to  it.  It  will  now 
be  necessary  to  identify  as  many  of  these  points  as  possible  on  other  photographs,  covering  the 
same  area,  and  these  are  similarly  marked  by  red  dots,  and  identical  points  are  given  the  same 
designation  by  number  or  symbol  in  red  ink. 

The  identification  itself  of  points  on  several  pictures  offers  no  serious  difficulties,  and,  with 
some  practice,  as  many  points  as  maybe  needed  for  a full  development  of  the  terrene,  even  under 
different  illumination  of  the  pictured  areas,  may  be  picked  out  with  rapidity  and  certainty. 

(e)  Application  of  Professor  Hauclds  method  for  the  identification  of  pictured  points. — In  cases 
of  doubt,  when  attempting  to  identify  the  same  point  on  two  different  photographs,  beginners 
may  take  advantage  of  Professor  Hauck’s  method,  which  has  been  described  in  Chapter  I, 
Paragraph  VII. 

The  two  photographs  are  pinned  side  by  side  on  a drawing  board.  The  images  of  the  camera 
stations  whence  the  pictures  were  obtained  are  “ kernelpoints,”  and  if  they  fall  outside  of  the 
picture  limits  they  are  determined  from  the  ground  plan  and  platted  on  the  drawing  board.  The 
parallels  to  the  principal  lines  of  the  photographs  on  which  the  scales  are  to  be  laid  off  are  drawn 
in  the  manner  explained  in  Chapter  I and  the  scales  are  fixed  in  position.  A fine  needle  is  now 
inserted  into  each  of  the  “kernelpoints”  and  the  loop  at  one  end  of  a fine  silk  thread  is  dropped 
over  each  needle,  the  other  end  of  the  thread  being  secured  by  a slender  rubber  band  to  a small 
paper  weight  (fig.  62). 

A well  defined  point  is  now  identified  on  both  photographs,  sufficiently  far  from  the  “kernel 
points,”  and  one  thread  is  moved  by  taking  the  paper  weight  up  and  passing  its  thread,  under 
gentle  tension  of  the  rubber  band,  through  the  point  just  identified  on  the  photograph,  when  the 
weight  is  deposited  upon  the  drawing  board,  holding  the  thread  in  the  given  position.  The  same 
operation  is  repeated  with  the  other  silk  thread  and  the  other  photograph,  when  the  two  threads 
should  intersect  the  scales  at  identical  division  marks.  If  they  do  not,  one  of  the  scales  is  to  be 
moved  until  botli  threads  bisect  the  same  division  marks  of  the  scales. 


686 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


jSow  the  identification  of  the  doubtful  points  may  be  proceeded  with.  Having  selected  a 
point  on  one  of  the  photographs,  the  corresponding  silk  thread  is  moved  to  bisect  that  point, 
noting  the  position  of  the  thread  with  reference  to  the  scale  in  this  position.  The  other  thread  is 
moved  to  bisect  the  corresponding  graduation  mark  on  the  second  scale,  when  this  thread  will 
also  bisect  the  corresponding  point  on  the  second  photograph. 

(/)  Flatting  the  intersections  of  horizontal  directions  to  pictured  points. — After  enough  pictures 
have  been  selected  to  control  the  cartographic  development  of  a certain  area  and  the  identification 
and  marking  of  corresponding  xioints  have  been  completed,  projections  of  all  these  x>oints  on  the 
horizon  lines  of  the  x>ictures  are  marked  (their  abscisste  are  measured)  and  transferred  to  the 
straight  edge  of  a strip  of  x>aper,  including  the  marking  on  the  paper  strip  of  the  principal  point 
of  every  xihotograph.  Each  paper  strip  bears  the  same  designation  (in  red  ink)  as  the  picture  to 

which  it  belongs. 

These  strijis  are  now  jilaced  uxi- 
on  the  platting  sheet  on  the  picture 
traces  to  which  they  belong  in  such 
a manner  that  the  principal  points 
of  paper  strips  and  picture  traces 
coincide,  and  in  this  position  they 
are  securely  held  to  the  working- 
sheet  by  means  of  small  thumb  tacks 
or  x>ax>er  weights. 

To  x>lat  the  horizontal  x>rojec- 
tions  of  a point,  shown  and  marked 
on  two  x>rints,  two  fine  needles  are 
inserted  into  the  idatted  station 
X>oints  I and  II , fig.  62  (of  the  two 
Xirints)  and  a fine  silk  thread  at- 
tached to  a small  x>aper  weight  w 
(by  fine  rubber  band  h)  is  secured 
to  each  needle  by  a loox>. 

The  thread  attached  to  station 
needle  I is  now  moved  over  the 
weighted  pax>er  strix>  (indicating  the 
picture  trace  on  the  x>lan)  until  it 
bisects  the  horizontal  x>rojection  a' 
of  the  picture  xioint  a.  The  weight 
is  now  placed  uxion  the  working 
X>lan,  holding  this  thread  (under 
slight  tension)  in  this  position.  The 
second  thread,  attached  to  the  nee- 
dle in  station  IT,  is  x>laced  over  the  xirojection  a"  of  the  image  of  the  point  A,  also  under  tension 
of  the  rubber  band.  The  xioint  of  intersection  of  the  two  threads  will  be  the  position  on  the  x>lan 
of  the  point  to  be  platted  (=  A). , After  this  position  of  A uxion  the  plan  has  been  checked,  in  the 
same  manner,  by  means  of  another  photograph  (thread  and  paper  strip)  taken  from  a third  station, 
TIT,  and  containing  the  image  a'"  of  the  xioint  A,  its  platted  position  is  marked  by  a dot  in  red  ink 
and  its  designation  corresxionding  with  that  given  on  the  x>rints  is  also  affixed. 

After  a sufficient  number  of  x>oints  have  been  platted  in  this  manner  by  intersections,  and 
after  they  have  all  been  supplied  with  the  letters  or  numerals  given  them  on  the  prints,  their 
elevations  are  determined  and  also  added  in  red  ink.  Frequently  the  designation  of  the  xioints 
by  letters  or  symbols  are  only  added  in  xiencil  on  the  working  sheet,  to  be  erased  after  the  eleva- 
tions of  the  points  have  been  affixed  to  them  in  red  ink. 

When  the  strixis  of  paper  should  overlap  each  other,  as  shown  in  fig.  63,  the  part  CD  of  the 
picture  trace  PQ  is  marked  off  on  the  strip  MN  lying  under  PQ , the  paper  strip  PQ  is  placed  in 
Xiroper  xiosition,  and  the  marks  on  its  edge  are  transferred  to  the  line  CD.  The  strix>  PQ  is  now 
placed  under  MN,  the  marks  on  the  latter  along  CD  serving  the  same  purpose  as  those  of  PQ. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


687 


When  a station,  A,  fig.  64,  falls  so  close  to  the  edge  of  the  working  board  that  the  trace  QB 
(of  the  picture  plane)  falls  outside  of  the  limits  of  the  plan,  then  the  trace  AC  of  the  principal  plane 
is  produced  to  B , making  AB  = AC  = focal  length  of  the  picture,  and  MN  is  drawn  perpendicular 
to  BC  or  parallel  to  QB.  The  line  MB  will,  with  reference  to  QB,  occupy  the  same  position  as 
the  focal  plane  of  the  camera  does  to  the  picture  plane  of  the  perspective.  The  direction  of  a 
point  of  the  photograph  projected  in  Q on  the  picture  trace  is 
found  by  joining  WA  and  producing  to  the  opposite  side  of  A. 

As  mentioned  before,  the  intersection  of  the  first  two  lines 
of  direction  should  be  checked  either  by  a third  line  or  other- 
wise before  the  position  on  the  plan  of  a pictured  point  should 
be  accepted  as  correct.  Such  intersections  may,  for  instance,  be 
checked  by  determining  the  height  of  the  point  from  both  photo- 
graphs. Unless  correctly  platted  and  correctly  identified,  the  two 
values  for  its  height,  will  not  agree.  This  check,  however,  does 
not  guard  against  slight  errors  in  platting.  A check  may  also  be 
obtained  by  drawing  a line,  on  which  the  point  is  situated,  with 
the  perspectograph  or  perspectometer,  but  the  best  check  will  al- 
ways be  a third  intersecting  line  of  direction  from  a third  station. 

(g)  Platting  pictured  points  iconometrically  by  vertical  intersec- 
tions.— We  had  seen  how  the  base  line  between  two  stations  is  projected  into  horizontal  plan  for 
the  method  of  horizontal  intersections  hitherto  considered,  but  when  two  camera  stations  are 
occupied  at  different  elevations  (and  close  together  horizontally)  to  locate  features  of  the  terrene 
by  intersections,  the  so-called  “method  of  vertical  intersections”  is  employed.  With  this  method 
the  base  line  (its  horizontal  projection  being  either  too  short  or  more  frequently  falling  into  the 
direction  in  which  the  points  to  be  located  iconometrically  are  situated)  is  projected  upon  a vertical 
plane.  The  greater  the  difference  in  elevation  between  the  two  stations,  the  greater  the  length  of 
this  base-line  projection  in  vertical  plane,  and  also  the  better  the  location  of  the  points  by  vertical 

intersections  will  be. 

We  will  have  with  reference  to  fig.  65: 

A and  B = positions  of  the  two  camera  stations,  platted 
upon  the  working  sheet.  (A  is  more  elevated  than  B). 
aB  = horizontal  projection  of  the  base  line  AB.  AN 
and  i?N  = two  negatives  (showing  the  images  dA  and  dB 
of  the  same  point  I))  exposed  at  the  stations  A and  B 
respectively.  HAKRAB'  and  RBRB'  = picture  traces  of  the 
two  negatives  on  the  ground  plane  or  working  sheet. 
aPA  =-  BPb'  = focal  length  of  the  negatives  AN  and  BK. 

We  will  assume  that  the  horizontal  plane  passing 
through  the  lower  station  (B)  is  the  ground  or  platting 
plane,  and  the  principal  plane  of  the  negative  A may  be 
taken  as  the  vertical  plane  of  projection.  RABR  AB'  will 
then  be  the  trace  of  the  picture  plane  AN  on  the  ground 
plane. 

Furthermore,  the  principal  plane,  of  which  aPA  is  the  trace  in  the  ground  plane,  is  supposed 
to  be  revolved  about  aPA  into  the  ground  or  platting  plane  in  order  to  simplify  the  construction. 

To  plat  the  position  in  the  ground  plane  of  a point  I),  pictured  on  AN  and  BN  as  dA  and  dB 
respectively,  the  rays  Adx  and  Bdn  are  projected  upon  the  vertical  plane  (revolved  about  aPA 
into  the  ground  plane)  when  (dQ,  hi  fig.  65,  will  represent  their  point  of  intersection  d,  projected 
into  the  vertical  plane  = d,,  and  revolved  about  aPA'  into  the  platting  plane  = (dQ. 

The  ray  AdA  — ATJ  intersects  or  penetrates  the  picture  plane  AN  at  a distance  = dAdAl / 
vertically  above  dA,  on  its  picture  trace  RABRAB'  (ground  line  of  picture  AN).  This  ordinate  is 
laid  off  upon  PARAB  = PA'  (dA),  when  (dA)  will  be  the  projection  on  the  vertical  plane  of  the 
pictured  point  dA. 

The  vertical  through  a projected  upon  the  vertical  plane  is  represented  as  a (A),  and  if  we 
make  a (A)  — PAPAB  (of  picture  AN)  = difference  in  elevation  between  the  two  stations  A and  B, 


Fi  g.  65 


688 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


then  (A)  will  be  the  upper  camera  station  A projected  into  the  vertical  plane,  and  the  line 
connecting  A with  the  point  (dA),  just  found,  will  be  the  projection  into  vertical  plane  of  the  ray 
AdA  or  AD  (revolved  about  aPA  with  the  vertical  plane  into  the  platting  plane). 

The  ray  BdB  — BD  intersects  the  second  picture  plane  1>N  in  dB.  If  we  draw  through  dB 
(projection  of  dB  in  ground  line  HBRB')  a perpendicular  to  aPA'  — dB'dlB,  then  dlB  will  be  the 
projection  into  the  vertical  plane  of  the  horizontal  projection  in  the  picture  trace  of  the  picture 


Ha  fl 

d' 

SnA  Ha 

1 

1 

1 

-067 


p'  a’ 

1 AB  AB 


H‘ 


O^B 

1 

1 

1 J* 

A°-  B r 

W S 

Hb 

’ h; 

point  dB.  Producing  dD'dlB  and  making  dlB  (dB)  = dRdB'  (measured  on  the  negative  jBn)  will  locate 
at  (dB)  the  projection  of  the  pictured  point  dB  upon  the  vertical  plane. 

The  perpendicular  to  aPA  through  B will  locate  the  projection  into  the  vertical  plane  =bx  of 
the  platted  station  B , hence  the  line  connecting  bx  with  (dB)  will  be  the  projection  into  the  vertical 
plane  of  the  ray  Bdn  — BD. 

The  intersection  (dx)  of  bx  (dB)  with  (A)  (dA)  locates  the  projection  into  vertical  plane  of  the 
point  sought,  d,  and  the  horizontal  projection  of  this  point  d (the  platted  position  of  the  original 
point,  D)  will  be  on  the  line  (dx)  dx  (which  is  the  vertical  through  d,  or  in  our  case  the 
perpendicular  to  aPA  from  (d,)),  and  either  horizontal  directions  adA  or  BdB,  produced  to  intersect 
tliis  perpendicular  (d,)  dx  will  locate  the  horizontal  projection  d'  of  the  point  d,  representing  the 
position  on  the  platting  sheet  of  the  point  D with  reference  to  the  platted  stations  a and  B.  (The 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


689 


location  of  d'  as  the  intersection  of  the  horizontal  directions  adf  and  Bda'  would  not  be  very 
accurate  for  our  case,  and  far  less  so  for  pictured  points  on  the  other  side  of  the  principal  point 
PB',  where  the  angles  of  intersection  of  the  horizontal  directions  would  be  even  smaller  than  at  d'.) 

The  point  dx  being  the  projection  into  the  vertical  plane  of  the  point  d'  (=  horizontal 
projection  into  the  ground  plane  of  the  point  d)  the  length  (dx)  df  measured  on  the  platting  scale, 
will  represent  the  elevation  of  the  point  I)  above  station  B. 

( h ) Iconometric  determination  of  elevations. — Generally  speaking,  one  perspective  will  not 
suffice  to  determine  the  height  of  a point,  although  there  are  exceptions,  like  the  points  on  the 
horizon  line,  which  have  the  same  elevation  as  the  camera  station. 

With  reference  to  fig.  66  we  have:  dx  = horizontal  projection  of  the  point  I>.  Bdx  = horizon- 
tal distance  between  platted  station  B and  platted  position  d of  point  D (measured  in  platting 
scale  on  working  sheet).  BdXli  — horizontal  distance  between  station  B and  projection  of  pictured 
point  dB  in  ground  line  HB  Ilf  measured  on  platting  sheet.  dXB  (dB)  = h — ordinate  of  pictured 
point  dB  above  ground  line  (revolved  with  vertical  plane  about  BdXa  into  platting  plane),  measured 


oil  picture.  dx  (d)  — 11  = height  of  point  d above  the  ground  plane  (revolved  into  the  ground  plane 
with  the  vertical  plane  about  Bdx).  Measured  on  the  platting  scale,  it  will  give  the  height  of  D 
above  the  camera  horizon  (ground  plane  = horizon  plane). 

The  height  II  is  a fourth  proportional  to  the  three  known  lengths  Bdh  BdUt,  and  d]B  (dB). 

Aftei  projecting  the  platted  point  d and  the  pictured  point  dR  into  the  principal  plane,  and 
after  i evolving  the  latter  about  the  principal  line  BP  into  the  platting,  or  ground  plane,  we 
will  have: 

^ (dB  ) h = height  of  pictured  point  dB  above  the  platting  plane.  ( d'B ) = pictured  point  dB, 
projected  into  the  principal  plane  and  revolved  with  the  latter  about  the  principal  line  into  the 
platting  plane,  (d')  df  = vertical  height  of  the  point  d,  projected  into  the  vertical  plane  and 
revolved  with  the  latter,  about  the  principal  line,  into  the  platting  or  horizon  plane;  hence  (d') 
d\  — 11  = elevation  of  d above  the  horizon  plane. 

This  height  = II  being  the  fourth  proportional  to  the  three  known  lengths: 

— focal  length  of  the  print.  P (da')  — ordinate  of  pictured  point  dv, 

6584 44 


measured  on 


690 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


photograph,  and  Bdf  =f+  Pd/;  where:  Pd/  = vertical  distance  between  the  platted  point  d,  and 
the  picture  trace  RaRf,  to  be  measured  on  the  platting  sheet,  its  value  ( =H)  may  be  found 
mechanically  with  aid  of  an  ordinary  sector,  fig.  67,  as  follows: 

Take  with  a pair  of  dividers  the  (ordinate)  distance  from  the  pictured  point  dB  to  the  horizon 
line  (on  the  photograph),  place  one  point  of  the  dividers  on  the  division  G of  the  sector,  fig.  67, 


point  of  the  dividers  coincides  with  the  corresponding  division  1)  of  the  other  arm  of  the  sector 
(OI>  being  equal  to  OG  = focal  length),  now  add  the  length  d/P,  fig.  66  (horizontal  distance  of  the 
platted  point  d\  to  the  picture  trace  HaHn'  projected  into  vertical  plane),  to  the  focal  length  = / 
= OG,  fig.  67,  by  placing  one  point  of  the  dividers  in  C , when  the  other  point  may  coincide  with 
the  division  A of  the  scale  OG.  Hold  the  sector  unchanged,  turn  the  dividers 
, about  the  point  A,  and  bring  the  second  point  to  the  graduation  mark  B of 
scale  OB,  B corresponding  to  A,  or  OB  = OA;  when  AB  will  represent  the 
height  R of  the  point  d above  the  horizon  plane  of  the  station  B,  to  be  meas- 
ured on  the  platting  scale. 

(i)  Iconometric  determination  of  elevations  by  means  of  the  so-called  “ scale  of 
heights. ” — Another  method  consists  in  making  use  of  the  “scale  of  heights,”  fig. 
68.  Make  BP  = /=  focal  length  of  the  perspective,  erect  PA  perpendicular  to 
SP  in  P,  and  divide  both  lines  into  equal  parts.  Draw  radials  from  S through 
the  points  of  division  on  PA,  and  through  those  of  SP  draw  parallels  to  PA. 
Now,  with  a pair  of  dividers  take  from  the  photograph  the  distance  from  the 
pictured  point  to  the  horizon  line  (the  ordinate  of  the  pictured  point  corre- 
sponding to  P(d'b)  = h,  in  fig.  66)  and  transfer  it  to  PA  from  P = P/u.  The 
position  of  //  may  be  found  to  correspond  to  the  line  S/i,  passing  through  the 
point  9 of  the  graduation  on  PA. 

With  a pair  of  dividers  take  now  (from  the  platting  sheet)  the  vertical 
distance  from  the  horizontal  projection  of  the  point  to  the  picture  trace  ( = dd[ 
in  fig.  66)  and  transfer  it  to  the  right  or  left  of  P according  as  the  point  of  the 
plan  falls  beyond  the  picture  trace  or  between  the  platted  station  and  the  pic- 
ture trace.  In  fig.  68  it  is  shown  as  falling  between  the  station  and  the  picture 
trace  into  m.  The  line  mB,  drawn  parallel  with  PA,  is  intersected  by  the  radial  S/t  (corresponding 
to  scale  division  mark  9)  in  M.  The  distance  mM,  measured  on  the  platting  scale,  will  be  the 
height  of  the  point  above  (or  below)  the  station. 

A scale,  fig.  69,  is  conveniently  pinned  somewhere,  perpendicularly  to  a line  AB,  the  division 
C of  the  scale,  corresponding  to  AB,  being  the  height  of  the  camera  station.  One  point  of  a pair 
of  dividers  with  which  the  length  AB  was  taken  off  the  “ sector,”  or  with  which  the  length  mM 


A 


Fi&.69 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


691 


was  taken  off  the  “scale  of  heights,”  is  set  in  C,  fig.  69,  and  the  division  mark  P of  the  scale, 
coinciding  with  the  other  point  of  the  dividers,  will  indicate  the  height  of  the  point  above  the 
plane  of  reference  or  datum  plane. 

This  height  is  entered  in  pencil  on  the  plan,  inclosed  in  a small  circle,  to  distinguish  it  from 
the  number  of  the  station.  It  is  checked  by  means  of  a second  photograph,  and  when  the 
discrepancy  between  the  two  values  for  the  elevation  of  the  point  is  within  the  permissible  limits 
of  error,  their  mean  value  is  entered  in  red  ink  on  the  plan  and  all  pencil  figures  are  erased. 

Any  marked  difference  in  the  value  for  the  height  of  a point  obtained  from  two  photographs 
would  indicate  either  that  the  two  points  selected  on  the  photographs  do  not  represent  the  same 
point  of  the  terrene,  or  that  an  error  in  platting  or  in  finding  the  height  had  been  made.  A third 
intersecting  line  from  a third  station  would  dispose  of  the  first  two  alternatives,  and  a new 
measurement  of  the  height  will  show  whether  an  error  had  been  made,  or  whether  the  discrepancy 
is  due  to  unavoidable  errors. 

(j)  The  use  of  the  so-called  “ photograph  hoard.11 — The  various  constructions  described  in  the 
preceding  pages,  if  made  directly  on  the  platting  sheet  and  on  the  photographs,  would  produce 
confusion  in  the  iconometric  platting,  owing  to  the  intricacy  of  the  lines,  and  would  obscure  many 
details  in  the  pictures.  Captain 
Devi  lie,  therefore,  has  had  a spe- 
cial drawing  board  prepared  on 
which  as  many  of  the  construc- 
tion lines  are  drawn,  once  for 
all,  as  would  have  to  be  repeated 
for  the  different  prints  of  uni- 
form size  and  which  had  been 
obtained  with  the  same  camera. 

This  so-called  “photograph 
board”  is  an  ordinary  drawing 
board,  covered  with  tough 
drawing  paper,  the  surface  of 
which  is  to  represent  alterna- 
tively either  the  picture  plane 
or  the  principal  i>lane  (both 
revolved  into  the  horizon 
plane).  It  is  used  in  conjunc- 
tion with  the  photographs  or 
negatives. 

Two  lines,  T)D'  and  88' , fig. 

70,  are  drawn  at  right  angles  to 
each  other.  They  represent  the 
horizon  and  principal  lines,  while  PI)  = PP‘  = PS'  —f  = focal  length,  so  that  D,  P',  8,  and  S'  are 
the  left,  right,  lower,  and  upper  distance  points,  respectively. 

The  photograph  is  placed  in  the  center  of  the  board,  the  principal  line  coinciding  with  SS'  and 
the  horizon  line  with  DP',  in  which  position  (TYZO)  it  is  secured  to  the  board  by  means  of 
small  thumb  tacks  or  pins.  The  four  scales,  forming  the  sides  of  the  square  OTYZ , serve,  among 
other  purposes,  to  locate  lines  parallel  either  with  88'  or  PI)'  (without  actually  drawing  the 
parallels)  on  the  photograph,  the  latter  falling  within  the  limits  of  the  square  OTYZ.  At  a 
suitable  distance  from  the  distance  point  I)'  a perpendicular  QR  is  drawn,  on  which  are  marked 
by  means  of  a table  of  tangents  the  angles  formed  with  PQ  by  lines  drawn  from  P.  This  scale 
may  be  used  for  measuring  the  altitudes  or  azimuthal  angles  of  points  of  the  photograph,  as  will 
be  explained  in  a separate  paragraph  later. 

From  8 as  a center  with  8P  —f  = focal  length  an  arc  of  a circle  PL  is  described  and  divided 
into  equal  parts.  Through  these  points  of  division,  and  between  PL  and  PD',  lines  are  drawn 
converging  to  8.  Parallels  MY  to  the  principal  line  are  also  drawn,  as  shown  in  fig.  70.  All  these 
lines  are  used  in  connection  with  the  scale  of  degrees  and  minutes  QR. 


Fig. 70 


692 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


The  studs  of  the  u centro  lineads”  (to  be  mentioned  later)  are  fixed  in  A,  B , C,  and  F,  the  lines 
AB  and  GE  joining  their  centers,  and  those  required  for  adjusting  the  centro  lineads  are  drawn 
on  the  photograph  board  to  be  used  as  will  be  explained  in  a later  paragraph.  The  square  FGKH 
is  constructed  on  the  four  distance  points  8,  S',  I)' , and  D. 

(k)  Construction  of  the  traces  of  a figure’s  plane. — If  one  wishes  to  use  a perspective  instrument 
for  converting  a figure — situated  in  an  inclined  plane  of  which  the  perspective  (photograph)  is 
given — into  the  projection  of  the  figure,  into  horizontal  plan,  it  will  be  necessary  to  locate  the 
traces  of  the  figure’s  plane  on  the  principal  and  picture  planes. 


FiG.71 


We  may  distinguish  between  two  cases  that  frequently  arise  in  practical  work. 

(1)  The  inclined  plane,  containing  the  figure,  may  be  given  by  the  line  of  greatest  slope,  or, 

(2)  The  inclined  plane  may  be  given  by  three  or  more  points. 

First  case : The  inclined  plane  containing  the  figure  is  given  by  its  line  of  greatest  slope;  this 
may  be  an  inclined  road,  the  drainage  line  of  a straight  valley,  the  trend  of  a torrent,  the  surface 
of  a live  glacier,  etc. 

This  line  of  greatest  slope  may  be  represented  on  the  plan  by  a line  ab,  fig.  71,  the  altitude  of 
a being  known. 

After  the  photograph  has  been  pinned  to  the  photograph  board,  the  ground  line  XY  is 
drawn,  taking  the  horizontal  plane  through  a as  the  ground  plane. 

On  the  platting  board  aO  is  drawn  through  a perpendicular  to  the  horizontal  projection  ab  of 
the  line  of  greatest  slope,  and  it  is  produced  to  its  intersections  L and  0 with  the  principal  line 
8\P\  and  with  the  picture  trace  X,  Y,. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


693 


On  the  photograph  pE  is  made  equal  to  pxb)  at  E a perpendicular  to  XY  is  erected  and 
produced  to  tlie  intersection  ft  with  the  pictured  line  of  greatest  slope. 

If  we  now  make  pX (on  the  photograph)  = pxo  (of  the  plan)  and  join  Nft  on  the  picture,  theline 
Nft  will  represent  the  trace  of  the  required  plane  (the  figure’s  plane)  on  the  picture  plane. 

If  pQ  (on  the  photograph)  is  made  equal  to  pxL  (of  the  plan)  and  ()  joined  with  M,  MQ  will 
represent  the  trace  of  the  required  plane  in  the  principal  plane,  revolved  about  SS'  (on  the  pho- 
tograph board)  into  the  picture  plane,  the  station  8 falling  in  D. 

Producing  MQ  to  B,  DU  will  represent  the  vertical  distance  of  the  station  8 above  the  plane 
EM  ft. 


Second  case:  The  inclined  plane  containing  the  figure  is  given  by  three  points. 

Take  for  ground  plane  the  horizontal  plane  containing  one  of  the  points  a,  fig.  72,  and  draw 
the  ground  line  XY  on  the  photograph.  On  the  platting  sheet  join  a to  the  two  remaining  points, 
b and  c,  and  produce  these  lines  ab  and  ac  to  the  intersections  E and  F with  the  picture  trace. 

On  the  photograph  make  pxK  equal  to  pE  and  draw  KL  perpendicular  to  XY.  Join  the 
perspectives  a and  ft  of  the  points  shown  in  a and  b on  the  plan  and  produce  to  the  intersection 
with  KL.  Make  pxT  equal  to  p F,  draw  TX  perpendicular  to  XY,  and  produce  to  the  inter- 
section N with  the  line  joining  the  perspectives  a and  y (of  a and  c).  Join  N and  X,  when  NL 
will  represent  the  trace  of  the  required  plane  on  the  picture  plane. 

Produce  LX  to  0 and  mak e pG  = pxO;  join  a and  G and  make  pxQ  = pH.  The  line  MQ  will 
represent  the  trace  of  the  required  plane  on  the  principal  plane,  revolved  about  SS1  into  the 
picture  plane,  the  station  8 being  nowr  in  I).  Here  again  Eli  is  the  vertical  distance  of  station  8 
above  the  plane  containing  the  three  given  points  a , b,  and  c. 


694 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


(1)  Contouring. — After  the  heights  of  a sufficient  number  of  points  have  been  determined  to 
give  a good  development  of  the  terrene  that  is  to  be  mapped,  the  contour  lines  are  drawn  in  by 
interpolation  between  the  points  of  which  the  elevations  had  been  established. 

In  a moderately  rolling  country  a limited  number  of  points  of  known  elevations  will  suffice 
to  draw  the  contour  lines  with  precision ; but  in  a rocky  region,  where  abrupt  changes  and  irregular 
forms  predominate,  it  is  almost  impossible  to  plat  enough  control  points  to  enable  the  iconometric 
draftsman  to  render  a faithful  representation  of  the  relief  of  the  broken  terrene,  and  it  is 
here  that  a close  study  of  the  photographs  will  give  the  greatest  assistance  in  modifying  the 
courses  of  the  contours  to  represent  the  characteristic  features  of  the  terrene. 

The  value  of  photographic  views  for  a correct  or  naturalistic  delineation  of  the  topography 
of  a given  area  is  generally  acknowledged  by  experienced  topographers,  even  when  using 


instrumental  methods  alone  for  the  control  work,  as  a minute  study  of  the  pictured  terrene  (the 
photographs)  will  always  aid  the  draftsman  (when  inking  the  topographic  sheet)  to  draw  the 
contours  (of  which  the  main  deflections  had  been  located  instruraeu tally)  with  a more  natural  and 
artistic  reproduction  of  nature’s  forms  than  could  be  attained  by  mechanically  inking  the  penciled 
lines  as  obtained  solely  by  instrumental  measurements. 

Instead  of  drawing  the  contour  lines  at  once  on  the  plan,  the  draftsman  may  begin  by 
sketching  them  on  the  photographs,  following  the  same  rules  for  their  location  as  if  he  were 
drawing  them  on  the  plan,  for  the  image  of  every  platted  point  is  already  marked  on  the  photo- 
graph and  its  elevation  may  be  taken  from  the  working  plan.  By  following  this  course  he  will  be 
enabled  to  follow  the  inequalities  of  the  surface  very  closely.  Those  perspectives  of  the  contours 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


695 


on  the  pictures  will  greatly  facilitate  their  horizontal  projections  to  be  drawn  upon  the  plan. 
They  may  also  be  transferred  to  the  plan  by  meaus  of  the  perspectograph  or  perspectometer  if 
accuracy  is  to  give  place  to  rapidity. 

A sufficient  number  of  tertiary  points  having  been  platted  by  intersections,  there  will  be  no 
difficulty  in  drawing  the  contour  lines  (by  interpolation)  between  such  points.  It  may  happen, 
however,  that  the  number  of  the  control  points  is  too  small  and  that  the  latter  are  too  far  apart 
to  give  a good  definition  of  the  terrene  (as  in  a topographic  reconnaissance),  and  then  it  will 
become  necessary  to  resort  to  other  (frequently  less  accurate)  methods  for  locating  the  contours 
on  the  plan. 

For  example,  the  ridge  a b c d of  a mountain  range  appearing  as  a /3  y 6 on  a photograph, 
fig.  73,  may  be  divided  by  the  contour  planes  by  assuming  it  to  be  contained  in  a vertical  plane. 


On  the  plan,  fig.  73,  we  produce  the  projection  ad  of  the  ridge  to  the  intersection  F with  the 
picture  trace  XxYx  and  draw  through  the  projection  Sx  of  the  station  SXC  parallel  to  ad. 

The  photograph  having  been  pinned  to  the  photograph  board,  take  from  the  principal  point 
P on  the  horizon  line  PV  = pxC  and  PG  = px F.  At  G place  the  scale  of  equidistances  perpendic- 
ular to  the  horizon  line,  the  division  at  G corresponding  to  the  height  of  the  station,  and  join 
the  marks  of  the  scale  to  the  vanishing  point  V. 

Having  now  the  successive  points  of  intersection  of  the  ridge  by  the  successive  contour  planes, 
their  distances  from  the  principal  line  SS' — their  abscissae— are  marked  upon  the  edge  of  a strip 
of  paper  in  the  usual  manner.  The  intersection  of  the  radials  from  $j  through  the  points  marked 
on  the  paper  strip  with  the  projection  a . . d of  the  ridge  a . . y will  give  the  intersections 

of  the  contour  lines. 


696 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


Should  the  mountain  have  rounded  forms  and  uo  well-defined  ridge,  the  visible  outline  on  the 
photograph  may  be  assumed  to  be  contained  in  a vertical  plane  perpendicular  to  the  liue  of  direc- 
tion drawn  to  the  middle  of  the  ridge  outline. 

The  construction,  fig.  74,  is  made  by  drawing  the  line  of  direction  SM  to  the  middle  of  the 
x'idge  outline  and  SV  perpendicular  to  SM.  ' On  the  plan  pi  Ml  is  made  = PM,  and  from  the  pro- 
jection a of  the  summit  a of  the  mountain  a perpendicular  ac  to  *Sj  il/j  is  drawn,  which  will  represent 
the  horizontal  projection  [ac)  of  the  pictured  outline  (ary);  it  is  produced  to  the  intersection  A 
with  the  picture  trace  Aj  Ylt  PQ  is  taken  (on  the  photograph)  equal  to piN  (on  the  plan),  and  the 
scale  of  equidistances  is  placed  at  Q perpendicular  to  the  horizon  line  DD' . The  division  mark  at 
Q corresponds  with  the  elevation  of  the  station  S,  and  the  points  of  division  corresponding  with 
the  contours  are  joined  to  V and  produced  to  their  intersections  with  the  outline  a ..  y.  The 
platting  is  done  as  in  the  preceding  case,  or  the  lines  of  direction  drawn  to  the  points  of  intersec- 
tion of  the  outline  ay  by  the  contour  planes  may  simply  be  platted  and  the  contour  lines  on  the 
plan  may  be  drawn  tangent  to  these  lines  of  direction. 

The  horizon  line,  containing  the  perspectives  of  all  points  having  the  same  elevation  as  the 

station,  represents  the  perspec- 
tive of  a contour  line  when 
the  camera  horizon  is  identical 
with  a contour  plane.  The 
iconometric  draftsman  should 
pay  particular  attention  to 
geologic  forms  and  to  the  origin 
of  topographic  features,  as  with- 
out such  applied  knowledge  a 
correct  interpretation  of  such 
forms  and  their  cartographic 
representation  would  require 
the  cartographic  location  of  a 
vast  number  of  control  points 
to  obtain  a faithful  represen- 
tation of  the  terrene  forms. 
Although  the  latter  iuay  often 
result  from  the  successive  or 
combined  actions  of  many  agen- 
cies, they  will  yet  have  similar 
recurrent  characteristic  shapes 
when  produced  by  the  same 
causes,  and  the  contours,  being 
the  means  for  delineating  the  cartographic  representation  of  the  terrene  shaped  by  identical 
agencies,  should  also  show  a corresponding  characteristic  similarity. 

(m)  The  photograph  protractor. — The  angle  included  between  the  liue  of  direction  (to  a point 
of  a photograph)  and  the  horizon,  or  the  principal  plane — the  vertical  or  altitude  and  the  hori- 
zontal or  azimuth  angle — is  sometimes  wanted. 

The  horizontal  angle  may  be  obtained  directly  on  the  photograph  board  by  joining  the  station 
S,  fig.  75,  and  the  projection  a (on  the  horizon  line)  of  the  pictured  point  a.  If  required  in  arc 
measure,  the  distance  Pa  may  be  transferred  to  the  principal  line  SS'  from  P = PG;  I)  is  joined 
to  Q and  produced  to  the  scale  of  degrees  and  minutes  PC,  where  the  graduation  mark  k indi- 
cates the  value  of  the  horizontal  angle  in  arc  measure. 

When  many  such  angles  are  to  be  measured,  tliehorizontal  scales  TY  and  OZ,  fig.  75,  may  be  divided 
into  degrees  and  minutes  by  means  of  a table  of  tangents,  using  as  radius  the  focal  length  SP. 

The  altitude  is  the  vertical  angle  at  S of  the  right-angle  triangle,  having  for  sides  Sa  and  acx. 
To  construct  it,  take  DF  = Sa,  draw  PE  parallel  with  and  equal  to  aa,  join  l>  and  E,  and  produce 
BE  to  the  .scale  BG  of  degrees  and  minutes. 

This  construction  will  be  facilitated  by  the  lines  already  drawn  on  the  photograph  board, 
fig.  70.  With  a pair  of  dividers  take  the  distance  (abscissa)  from  the  pictured  point  a to  the 


Fi  g.  /5 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


697 


principal  line  88',  fig.  75,  and  carry  it  from  P,  fig.  70,  in  the  direction  PD',  and  from  the  point  so 
obtained  take  the  distance  to  the  arc  ML,  fig.  70,  measuring  in  the  direction  of  the  radials  marked 
on  tiie  board,  which  will  represent  the  distance  PF,  fig.  75.  Then,  with  the  dividers,  carry  aa  to 
FE,  fig.  75,  which  is  that  one  of  the  parallel  lines  MN  of  fig.  70  that  corresponds  to  the  point  F. 
The  construction  may  now  be  completed  in  the  manner  already  explained. 

A protractor  may  be  constructed  to  measure  these  angles  directly  by  drawing  lines  on  a 
transparent  plate  parallel  with  the  principal  line — they  contain  points  having  identical  azimuths — 
and  curves  containing  points  of  identical  altitudes. 

The  azimuthal  lines  may  be  found  by  platting  the  horizontal  angles  in  8,  fig.  70,  and  drawing- 
lines  parallel  to  the  principal  line  SS'  through  the  points  of  intersection  of  the  radials  with  the 
horizon  line  DD‘ . 

If  we  regard  the  horizon  and  principal  lines  as  axes  of  coordinates  and  denote  the  altitude 
aa  of  a point  a pictured  as  a,  fig.  75,  by  li,  the  equation  of  the  curve  of  altitude  h may  be  written — 

y2  = {x2  +f 2)  tan2  h. 

This  also  is  the  equation  of  an  hyperbola  of  which  the  principal  and  horizon  lines  are  the 
transverse  and  conjugate  axes,  and  of  which  the  principal  point  is  the  center. 

One  of  the  hyperbola’s  branches  represents  the  points  above  the  horizon,  and  the  other 
branch  the  points  of  equal  altitude  below  the  horizon.  The  asymptotes  are  lines  intersecting 
each  other  at  the  principal  point,  and  including  angles  with  the  horizon  line  equal  to  h.  This 
hyperbola  represents  the  trace  on  the  picture  plane  of  the 

cone  of  visual  rays  which  include  the  angle  h with  the  t-J_l  I 1 I I I 1 I I I I LD-P-t 

horizon  plane.  __ 

These  hyperbolic  curves  of  equal  altitude  may  be  — rr: 

obtained  by  computation,  using  the  preceding  formula  and  — -r 

substituting  different  values  for  li,  or  they  may  be  obtained 

graphically  by  platting  a series  of  points  for  each  curve  ~Y~ 

by  reversing  the  construction  given  above  for  finding  the  

altitude  of  the  pictured  point  a,  fig.  75.  The  angular  dis-  - — 

tance  between  the  lines  representing  points  of  equal  azi-  cr— ~~~~~~~ 
rnuths  (or  those  of  equal  altitudes)  will  depend  upon  the  brl  Ml  II  I I 11  ~Tl  Ti — 

degree  of  precision  required.  Fig. 76 

The  complete  protractor  is  shown  in  fig.  76.  It  may 
be  made  in  the  same  manner  as  mentioned  for  the  perspectometer  by  drawing  it  on  paper  on  a large 
scale,  reducing  it  by  photography,  and  making  a transparency  by  bleaching  in  bichloride  of  mercury. 

(4)  Method  of  V.  Legros  for  determining  the  position  of  the  horizon  line. — Commandant  V. 
Legros  recommends  the  use  of  these  hyperbolas  for  locating  the  horizon  line  of  a vertically 
exposed  photographic  plate: 

When  a camera  with  the  photographic  plate  adjusted  in  vertical  plane  is  rotated  horizontally 
in  azimuth,  the  plate  remaining  vertical,  any  point  a,  fig.  76,  will  describe  a hyperbola  aa'  on  the 
ground  glass  plate.  The  nearer  the  observed  point  a approaches  the  horizon  line  the  smaller  the 
curvature  of  its  hyperbolic  trace  on  the  ground  glass  will  become,  and  a point  a0  which  traverses 
the  ground  glass  plate  in  a straight  line  HR'  will  have  the  same  elevation  as  the  second  nodal 
point  of  the  camera  lens.  Its  angle  of  elevation  will  be  ± 0 or  HR'  will  be  the  horizon  line  of 
the  plate.  To  locate  the  horizon  line  experimentally  in  this  way  the  ground  glass  plate  is  best 
provided  with  a series  of  equidistant  horizontal  and  vertical  lines,  after  the  manner  of  Dr.  Le 
Eon’s  ground  glass  plates. 

(5)  Method,  of  Prof.  8.  Finsterw alder  for  locating  contours  on  the  plan. — Prof.  S.  Finsterwalcler’s 
method  for  the  iconometric  location  of  horizontal  contours  is  based  upon  the  following  considera- 
tion : 

The  pictured  outline  of  a terrene  form  is  regarded  as  the  trace  of  the  terrene  surface  in  a 
plane  vertical  to  the  platting  or  ground  plane  and  containing  the  pictured  outline.  This  method 
is  well  adapted  for  the  development  of  the  terrene  forms  of  a moderately  rolling  country. 

The  camera  stations  are  specially  selected  with  reference  to  the  use  of  this  method,  with  a 


p-7 

A 

P 

ctl 

a- 

-o 

Fig. 76 


G98 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


view  toward  obtaining  pictures  with  a sufficient  number  of  such  outlines  of  the  terrene  forms  to 
enable  the  icouometric  draftsman  to  give  a good  definition  of  tlie  relief  of  the  region  to  be 
platted. 

The  pictured  outlines  of  terrene  forms  may  be  regarded  as  falling  within  vertical  planes,  and 
the  rays  from  the  point  of  view — seeoud  nodal  point  of  camera  lens — to  the  pictured  points  of 
such  outline  will  form  a cone  with  apex  in  the  point  of  view,  its  base  being  formed  by  the  pictured 
outline. 

Any  horizontal  plane  containing  a contour  A will  intersect  such  a cone  of  rays  in  a curve  it, 
the  latter  touching  A in  one  point.  This  curve  B may  be  platted  on  the  working  sheet  by  laying 
off,  upon  a few  rays  from  the  platted  station  to  points  of  the  pictured  outline,  the  distance: 

It  cot  ft 

and  the  points  thus  located  on  the  radials  from  the  station  point,  if  connected  by  a continuous  line, 
will  represent  the  curve  B platted  in  horizontal  plan. 

h= difference  in  elevation  between  the  station  (whence  the  picture  was  taken)  and 
the  horizontal  contour  A. 

/j=vertical  angle  to  each  point  of  the  outline  bisected  by  the  vertical  plane  passing- 
through  its  radial  or  visual  ray. 

The  direction  of  the  pictured  outline  is  now  platted  on  the  plan,  and  where  it  bisects  the  curve 
B will  be  a point  of  the  contour  A.  As  we  naturally  would  draw  not  only  one  curve  f?,  but  rather 
a series  of  them  corresponding  to  several  horizontal  planes,  passing  through  a.  series  of  contours 
A of  various  elevations,  the  construction  may  be  simplified,  inasmuch  as  the  curves  B — being  lines 
of  intersection  of  the  same  cone  of  rays  with  a series  of  parallel  (horizontal  contour  planes)  planes — 
will  all  be  similar  in  shape,  their  corresponding  points  (points  on  the  same  radials)  having  the  same 
relative  positions  with  reference  to  the  platted  station,  the  value  h cot  ft  need  only  be  determined 
for  one  point  of  the  other  curves  B if  one  curve  B had  been  drawn,  the  others  being  parallel  with 
the  first. 


CHAPTER  IV. 


PHOTOGRAMMETERS. 

The  practical  value  of  a photogrammeter  (photographic  surveying  instrument)  depends  greatly 
upon  the  quality  and  general  uniformity  of  its  lens  or  lenses,  upon  the  rigidity  ot  the  component 
parts  of  the  apparatus,  its  easy  transportability,  and  on  the  rapidity  with  which  it  may  be  put 
into  adjustment. 

A good  phototopograpliic  lens  should  be  free  from  spherical  aberration  (or  diffusion  ot  the 
light  rays);  it  should  possess  no  chromatic  aberration,  nor  should  the  image  show  distortion  of 
any  kind,  and  the  field  of  view  (the  range  of  lens)  should  be  large,  rapidity  of  the  lens  being 
desirable,  but  less  important  than  the  other  requirements  just  mentioned. 

The  principal  lenses  in  use  for  phototopograpliic  purposes  are : Dallmeyer's  rapid  rectilinear, 
SteinheiVs  aplanat,  Bush's  pantoscopic,  Gorz’s  double  anastigmat,  and,  more  recently,  Zeiss's  anas- 
tigmat  lens. 

The  nodal  points,  the  focal  length,  arc  of  visibility,  and  the  arc  which  is  perfectly  free  from 
distortion  of  every  kind  should  be  known  for  every  lens  used  for  photo  topographic  purposes, 
and  the  manufacturers  of  all  good  lenses  are  best  fitted  to  determine  those  values  with  great 
precision  for  every  lens. 

I.  REQUIREMENTS  TO  BE  FULFILLED  BY  A TOPOGRAPHIC  SURVEYING  CAMERA. 

A good  surveying  camera  or  photogrammeter  for  topographic  work  should  produce  negatives 
which  are  geometrically  true  perspectives  the  elements  of  which  should  be  known,  and  the  follow- 
ing desiderata  should  be  fulfilled : 

First.  The  plates  to  be  exposed  should  be  adjustable  into  vertical  plane. 

Second.  The  distance  between  image  point  and  sensitive  plate  should  be  maintained  unchanged 
for  all  plates. 

Third.  This  distance — the  constant  focal  length — should  be  known  or  will  have  to  be 
determined  for  every  instrument. 

Fourth.  Means  should  be  provided  to  trace  or  locate  the  horizon  line  upon  every  negative  or 
print. 

Fifth.  Means  should  be  provided  for  locating  the  principal  point  upon  every  negative. 

Sixth.  A ready  orientation  of  the  photographs  (the  picture  traces)  for  iconometric  platting 
should  be  provided  for ; and  we  may  add  as 

Seventh.  Enough  characteristic  stations  (besides  the  triangulation  points  needed  for  the 
instrumental  control)  are  to  be  occupied  with  the  surveying  camera  to  give  a full  development  of 
the  terrene,  which  is  to  be  mapped. 

Until  recently  photographic  surveying  instruments  were  not  procurable  in  open  market. 
^Nearly  every  observer  who  made  practical  application  of  the  photographic  methods  for  topo- 
graphic surveys  had  an  apparatus  constructed  for  his  particular  need  and  according  to  his 
individual  ideas. 

In  the  following  we  will  describe  such  photogrammeters  as  may  be  regarded  as  special 
types,  constructed  to  fulfill  different  requirements. 

II.  ORDINARY  CAMERAS  ADAPTED  FOR  SURVEYING  PURPOSES. 

These  cameras  are  generally  supported  by  three  leveling  screws,  and  they  are  provided  with  a 
circular  level,  or  with  two  cross  levels,  for  adjusting  the  sensitive  plate  into  vertical  plane.  The 
distance  between  lens  and  sensitive  plate  (focal  distance)  may  be  made  invariable  by  means  of 

699 


700 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


two  rods  Sp,  fig.  77  ( Werner's  apparatus,  made  by  It.  Lecfiner,  of  Vienna,  in  Austria),  or  by  means 
of  two  arms  H and  clamp  screw  M,  after  the  bellows  had  been  extended  by  aid  of  the  pinion  K 
and  rack  movement  to  that  point  indicated  by  the  vernier  n,  fig.  78,  as  the  proper  focal  length  for 


infinite  distance.  The  arrangement  shown  in  fig.  78,  represents  the  apparatus  of  Dr.  Vogel  and 
Professor  Doergens , made  by  Stegemaun,  of  Berlin,  in  Prussia. 

Dr.  G.  Le  Bon  also  used  a similarly  modified  camera  for  his  archaeological  researches  in  India 
(undertaken  under  the  auspices  of  the  French  ministry  of  culture). 

Short  brass  points  ill,  fig.  79,  serve  to  locate  the  horizon  and  principal  lines  on  the  negatives  by 

protecting  the  sensitive  plates  against  the  action  of  those 
light  rays  which  they  intercept.  In  some  instances  those 
points  M may  be  brought  into  direct  contact  with  the 
sensitive  film  surface  of  the  plate  by  turning  a button, 


Fig.  79 


Fi  G. 80 


thus  producing  a sharp,  well-defined  image  of  the  outlines  of  the  teeth  on  the  negative. 

The  use  of  such  modified  cameras  should  not  be  extended  beyond  preliminary  work;  for 
extensive  use  the  results  will  not  be  sufficiently  uniform  and  accurate. 


U.  S.  Coast  and  Geodetic  Survey  Report  for  1897.  Appendix  No.  10. 


No.  82. 


CANADIAN  (E.  DEVILLE’S)  SURVEYING  CAMERA. 


U.  S Coast  and  Geodetic  Survey  Report  for  1897  Appendix  No  10. 


No  83 


d\ 


' !>rn 


4" 


CANADIAN  <E.  DEVILLE’SI  SURVEYING  CAMERA  — VERTICAL  POSITION. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


701 


III.  SPECIAL  SURVEYING  CAMERAS  WITH  CONSTANT  FOCAL  LENGTHS. 

(. 1 ) Dr.  A.  Meydenbaur1  s surveying  camera. — Among  the  numerous  patterns  of  this  class  of 
instruments  Dr.  Meydenbaur’s  is  probably  the  earliest  form.  Fig.  80  shows  Meydenbaur'1  s new , small- 
sized magazine  camera.  The  plates  are  successively  pressed  against  a metal  frame  secured  at  a 
constant  distance  from  the  lens.  After  an  exposure  the  plate  is  dropped  into  a leather  sack  b,  fig. 
81,  attached  to  the  camera.  The  dimensions  of  the  camera  box  are  9 by  12  centimetres,  it  weighs 
750  grammes,  and  it  is  mounted  on  a rod  which  is  joined  at  its  lower  end  to  three  short  legs  in 
such  a way  that  the  four  pieces  may  be  folded  together  to  form  a stout  cane  085  metre  long.  The 
lower  ends  of  the  three  legs  of  this  tripod,  and  the  upper  end  of  the  supporting  rod  are  con- 
nected by  twisted  violin  strings  to  which  tension  may  be  given  by  turning  the  ratchet  wheels 
indicated  in  fig.  81.  The  leather  pouch,  together  with  twelve  plates,  weigh  about  500  grammes. 

The  sensitive  plate  may  be  adjusted  into  vertical  plane  by  means  of  a ball  and  socket  connec- 


tion between  the  camera  and  upper  end  of  the  tripod  rod,  together  with  the  circular  level  L,  shown 
on  the  upper  face  of  the  camera  box  in  fig.  81. 

(2)  E.  Devilled  new  surveying  camera. — The  following  description  of  the  new  Canadian  survey- 
ing camera  is  taken  from  Deville's  Photographic  Surveying , Ottawa,  1895.  This  camera  is  shown  in 
figs.  82  and  83.  Figs.  81  and  85  represent  sections  of  the  instrument. 

The  camera  proper  is  a rectangular  metal  box  AB  (figs.  81  and  85)  open  at  one  end.  It  carries 
the  lens  L and  two  sets  of  cross-levels  (7(7,  whicli  may  be  observed  through  openings  in  the  outer 
mahogany  box.  The  metal  box  is  supported  by  wooden  blocks  and  a frame  FF,  held  in  position 
by  two  bolts  DD. 

The  plate  holder  is  made  for  single  plates;  it  is  inserted  into  the  carrier  EE,  which  may  be 
moved  forward  and  backward  by  turning  the  screw  G. 

A folding  shade  IIII,  hooked  to  the  front  of  the  camera,  and  diaphragms  KK,  inside  of  the 
metal  box,  intercept  all  light  that  does  not  contribute  to  the  formation  of  the  image  on  the  photo- 
graphic plate. 


702 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


The  camera  rests  on  a metal  triangular  base , fig.  86,  with  three-foot  screws,  exactly  like  the  base 
of  the  transit  which  is  used  in  conjunction  with  Deville’s  camera,  so  that  either  camera  or  transit 
may  be  placed  on  the  same  tripod  at  any  time.  The  camera  may  be  set  up  with  the  longer  side 
either  horizontal  or  vertical,  figs.  82  and  83.  Both  transit  and  tripod  are  carried  by  the  surveyor, 
Avhile  one  camera  with  one  dozen  plates  (in  the  single  plate  holders),  without  a tripod,  are  taken 
by  one  of  the  men  who  always  accompany  the  surveyor.  The  assistant  surveyor  has  a second 
camera,  with  12  plates  and  a separate  tripod. 

The  legs  of  these  tripods,  when  folded  together,  are  20  inches  long  and  are  placed  under 

the  box  of  the  transit,  in  a separate  sole  leather  case,  to  be  carried 
on  the  back  of  the  surveyor.  The  tripod  of  the  assistant  surveyor’s 
camera  is  similarly  attached  to  the  sole-leather  case  of  his  camera. 

The  lens  of  this  camera  is  a Zeiss  anastigmat,  No.  3 of  series  V, 
focal  length  = 141  millimetres  with  a deep  orange  color  screen  in 
front. 

Having  set  the  camera  up  on  the  tripod,  the  plate-holder  carrier 
E is  moved  back  as  far  as  it  will  go  by  turning  the  screw  G,  the 
plate  holder  is  inserted  through  the  opening  ME,  the  slide  is  with- 
drawn, and  the  carrier  is  moved  forward  by  revolving  the  screw 
G,  until  the  plate  is  in  contact  with  the  back  of  the  metal  box  AB. 
In  order  to  secure  a perfect  contact,  the  carrier  has  a certain  amount 
of  free  motion.  The  camera  should  now  be  turned  in  the  proper 
direction ; the  field  embraced  by  the  plate  is  indicated  by  lines  drawn  on  the  outside  of  the  mahogany 
box.  The  camera  is  now  carefully  leveled,  the  exposure  made,  and  the  plate  holder  withdrawn 
(after  the  slide  had  been  inserted)  by  repeating  the  same  operations,  however,  in  the  inverse  order. 

The  levels  CG  are  rigidly  attached  to  the  metal  camera  box  without  any  means  of  adjustment. 
They  are,  however,  very  nearly  adjusted  by 
the  maker.  For  this  purpose  he  takes  the 
metal  box  out  of  the  mahogany  casing  aud 
places  it  on  a piece  of  plate  glass  which  had 
been  leveled  like  an  artificial  horizon.  By 
filing  down  one  end  or  the  other  of  the  level’s 
outer  case  he  brings  each  bubble  very  nearly 
into  the  middle  of  its  tube.  These  tubes  have  continuous  numbers  on  the  graduation  marks,  as 
illustrated  in  fig.  87. 

Accompanying  each  camera  is  a piece  of  plate  glass,  \ inch  thick  and  11  inches  long,  which  can 
be  inserted  into  the  carrier  in  idace  of  the  plate  holder.  That  end  of  the  plate  glass  which  projects 
outside  of  the  camera  when  it  is  thus  inserted  is  coated  on  the  back  with  a varnish  of  gum  guaia- 

cum  (dissolved  in  alcohol)  to  which  some  lampblack  has 
been  added.  This  coating  has  very  nearly  the  same  re- 
fractive index  as  glass,  precluding  all  reflections  from  the 
back  of  the  plate  glass. 

When  the  camera  is  received  from  the  maker  the  exact 
readings  of  the  levels,  CG,  when  the  back  of  the  metal  box 
(against  which  the  photographic  plate  is  pressed)  is  verti- 
cal, should  be  ascertained.  To  do  this  the  bolts  P , fig.  85, 
next  to  the  opening  ill,  are  unscrewed  and  removed.  Q may 
The  piece  of  coated  plate  glass  is  now  inserted  into  the  car- 
rier E,  figs.  84  and  83,  and  pressed  into  contact  with  the  metal  box  by  revolving  the  screw  G.  The 
camera  is  placed  on  its  tripod  and  leveled.  Immediately  in  front  and  at  the  same  height  as  the 
camera  a transit  (or  a leveling  instrument)  T,  fig.  88,  is  set  up,  and,  after  carefully  adjusting  it,  a 
distant  but  well-defined  point  P is  selected  on  the  same  level  with  the  transit  and  camera.  The 
intersection  of  the  threads  of  the  telescope  is  brought  to  coincide  with  P,  and  the  telescope  is 
clamped  in  this  position  to  the  vertical  circle.  Turning  it  in  azimuth  the  image  of  P,  reflected 
by  the  plate  glass,  should  appear  at  the  intersection  of  the  telescope’s  threads.  If  it  does,  the 
face  of  the  plate  glass  is  vertical  and  the  position  of  the  bubble  in  the  tube  of  the  level,  directed 


then  slide  backwards  and  betaken  out. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


703 


at  right  angles  to  the  plate  glass,  is  the  correct  one  for  adjusting  the  instrument  in  the  future.  If 
it  does  not,  the  camera  must  be  tilted  forward  or  backward  by  means  of  the  foot  screws  until 
coincidence  is  established.  The  bubble  of  the  level  may  or  may  not  now  be  in  the  middle  of  the 
tube,  but  its  position,  whatever  it  is,  will  be  the  correct  one  for  the  future  when  adjusting  the 
camera  at  any  station.  This  level  reading  should  therefore  be  recorded,  and  whenever  the  camera 
is  to  be  leveled  in  its  subsequent  use  it  must  be  remembered  that  the  bubble  is  to  be  given  the 
same  position. 

This  level  reading  determination  is  to  be  made  for  the  two  positions  of  the  camera  in  which 
it  is  used,  tigs.  82  and  83,  horizontal  and  vertical. 

The  next  step  is  to  locate  the  position  of  the  principal  point  on  the  vertical  photographic  plate, 
and  to  determine  the  length  of  the  distance  line  or  the  constant  focal  length. 

Select  a station  so  that  a number  of  distant  and  well-defined  points  may  be  found  on  the 
horizon  line,  as  laid  down  by  the  maker  of  the  camera.  The  view  selected  may  be  the  distant 
shore  of  a lake,  a large  building,  or  a row  of  buildings.  Set  up  the  tripod  and  adjust  the  transit. 
Find  two  points  E and  F,  fig.  89,  on  the  horizon  line  (with  a zenith  distance  of  90°)  that  both  come 
within  the  field  of  the  camera,  when  set  horizontal,  both  points  being  near  the  edges  of  the  plate. 
Measure  the  angle  go  between  them. 

Find  two  other  points  G and  H , also  on  the  horizon  line,  and  such  a distance  apart  that  they 
both  come  within  the  field  of  the  camera  when  the  same  is  vertical,  fig.  83.  Now  replace  the 


G and  IT,  level  carefully  and  expose  another  plate.  The  first  plate,  after  development,  will  show 
the  two  points  E and  F on  a line  very  nearly  parallel  to  the  edges  AB  and  CD , fig.  89,  of  the  metal 
box.  The  principal  point,  of  course,  will  be  on  this  line.  Out  this  line  into  the  film  with  a fine 
needle  point  and  straightedge. 

The  second  plate,  exposed  in  the  vertical  position,  after  development  gives  another  horizon 
line  Gif  fig.  89,  which  may  be  transferred  to  the  first  plate  by  means  of  the  distances  AK,  and 
CL  to  the  corners  of  the  metal  box.  This  (principal)  line  is  likewise  cut  through  the  film  with 
a fine  needle  point  and  straightedge,  the  principal  point  P is  at  the  intersection  of  both  lines 
EF  and  GH. 

The  length  ot  the  distance  line,  SP  =/,  fig.  90,  may  be  computed  from  the  observed  horizontal 
angle  included  between  SB  and  SF,  and  from  the  distances  EP  = a and  PF  = h,  measured  on 
the  uegative. 

Let  <S',  fig.  90,  be  the  second  nodal  point  of  the  camera  lens,  a and  ft  the  angles  ESP  and  PSF. 

(X  ft  = GO, 

The  lengths  ot  a and  h are  known  and  it  we  designate  the  focal  length  SP  by  f we  will  have: 

tan  a — a 

f 

tan  ft  — ^ 
f 

tan  a X tan  ft  = 

P 


704 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


Hence: 


tan 


a b 
/*  f 

(a  -f-  /j)  = tan  = % A-  or: 

1 — ab 

P 

= l>  f~  = 0 

tan  oo" 


after  resolving  this  quadratic  equation  we  find: 


a -f  b 
2 tan  go 


+ 


yj 


(a  + by 

4 tan2  cj 


+ ab 


Having  found  the  focal  length  and  the  principal  jioint,  reference  marks  are  to  be  made  on  the 
edges  of  the  metal  box  to  indicate  the  horizon  line,  the  principal  line,  and  the  focal  length  on  the 
negatives,  or  on  the  enlargements  made  from  the  latter. 

Measure  the  distance  m,  fig.  89,  from  P to  AC.  From  the  corresponding  corners  A and  6’, 
fig.  91,  of  the  metal  box,  lay  off  m on  AR  and  CT.  With  a very  fine  and  sharp  file  held  in  the 
direction  of  the  lens,  cut  into  the  edge  of  the  metal  a clean  and  sharp  notch  at  Tand  another  at  R. 

Repeat  the  same  operation  at  the  corners  A and  B , fig.  91,  with  the  distance  n from  P to  AB, 
fig.  89. 

The  lines  OQ  and  RT  will  be  the  horizon  and  principal  lines  of  the  negatives  when  the  camera 
is  leveled  to  bring  the  bubble  into  its  proper  position,  as  has  been  mentioned  in  the  foregoing. 

From  R and  T,  fig.  91,  lay  olf  the  distances  Rr , Rr',  Tt , TV  = t = one-half  of  the  constant 
focal  length. 

' From  O and  Q measure  Oo,  Oo',  Qq,  Qq'  = 4 = one-fourth  of  the  focal  length,  and  at  each  one 

of  these  points  make  a notch  with  the  file  held  in  the  direction  of  the  lens. 

Every  photograph  will  now  show  twelve  triangular  projections  into  the  dark  border  of  the 


photograph.  Four  of  these  projections  serve  to  fix  the  horizon  and  principal  lines;  the  remaining 
eight  give  the  focal  length  value. 

It  now  remains  necessary  to  find  the  correct  readings  of  the  transverse  levels  (those  placed 
parallel  with  the  sensitive  plate),  when  the  horizon  and  principal  lines  pass  exactly  through  their 
notches  of  the  metal  box. 

Again  set  up  the  camera  facing  the  same  distant  view  as  before,  but  in  adjusting  it  bring  the 
bubble  of  the  transverse  level  near  one  end  of  the  tube,  note  the  level  reading  and  expose  a plate. 
After  development  it  will  give  an  horizon  line  EE,  fig.  92,  cutting  the  border  of  the  negative  in  A 
and  B at  some  distance  from  the  pictured  notches  0 and  Q.  Now  change  the  adjustment  ot  the 
camera  by  bringing  the  bubble  of  the  transverse  level  to  the  other  end  of  the  tube,  note  the  level 
reading  and  expose  another  plate.  This  will  give  another  horizon  line  E'  F' , cutting  the  border  ot 
the  negative  in  C and  D. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


705 


Great  care  should  be  exercised  in  both  cases  to  maintain  the  other  level  (the  one  at  right 
angles  to  the  sensitive  plate)  at  its  proper  reading  in  order  to  expose  both  plates  in  vertical  plan. 

After  measuring  GO  and  OA  or  BQ  and  QJ),  a simple  proportion  will  give  the  proper  reading 
of  the  transverse  level,  which  will  bring  the  horizon  line  of  the  vertically  exposed  plate  through 
the  two  notches  0 and  Q of  the  metal  box. 

The  correct  reading  of  the  other  transverse  level  is  found  by  the  same  method,  with  the  camera 
in  the  vertical  position,  fig.  83. 

All  these  operations  must  be  executed  with  great  care  and  precision,  and  with  the  help  of  a 
microscope  of  moderate  power,  as  the  subsequent  iconometric  platting  of  pictured  points  is  based 
upon  the  determination  of  the  ordinates  and  abscisste  of  such  points  on  the  photographs,  with 
reference  to  the  principal  and  horizon  lines,  as  a system  of  rectangular  coordinates. 

It  had  been  assumed  that  the  levels  were  placed  very  nearly  in  correct  adjustment  by  the 
maker,  as  previously  mentioned.  If  found  too  much  out,  they  should  of  course  be  lirst  approxi- 
mately adjusted  by  settiug  the  metal  box  on  a leveled  plate.  For  this  purpose  the  plate  glass  sent 
out  with  every  instrument  is  set  on  the  camera  base  aud  leveled  like  an  artificial  horizon. 

(5)  Use  of  the  instruments  comprised  in  the  Canadian  phototopographic  outfit. — The  instruments 
and  tripod  being  made  as  light  as  possible,  steadiness  is  secured  by  a net  suspended  between  the 
tripod  legs  in  which  a heavy  stone  is  placed.  With  this  device  better  photographs  and  more  pre- 
cise observations  are  obtained,  and  there  is  no  risk  of  the  instruments  (resting  upon  the  tripod) 
being  blown  over  during  one  of  the  sudden  and  strong  gusts  of  wind  so  frequently  encountered 
on  elevated  peaks  in  the  mountains. 

After  having  arrived  at  a triangulation  station,  the  surveyor  adjusts  the  transit  and  observes 
the  azimuth  and  zenith  distances  of  all  signals  marking  the  triangulation  and  camera  stations 
that  may  be  visible  from  his  position.  If  accompanied  by  his  assistant,  each  reads  one  vernier 
and  both  enter  the  readings  in  record  books.  After  completion  of  the  observations  they  compare 
notes.  Any  discrepancy  that  may  be  discovered  in  the  recorded  data  is  corrected  on  the  spot. 

The  camera  is  carried  in  a sole-leather  case  containing  also  twelve  filled  plate  holders.  When 
more  plates  are  needed  they  (with  the  necessary  holders)  must  be  carried  in  a separate  receptacle. 
Taking  the  camera  out  of  the  case,  the  leveling  base,  tig.  86,  is  screwed  to  it,  and  the  camera  is 
then  placed  upon  the  tripod,  from  which  the  transit  had  been  removed,  without  disturbing  the 
position  ot  the  tripod;  the  shade  or  hood  is  now  unfolded  and  attached  to  the  hooks  at  the 
front  of  the  camera,  fig.  82.  A plate  holder  is  inserted  into  the  carrier,  and  its  number  is  recorded 
upon  a rough  outline  sketch  of  the  view  commanded  by  the  field  of  the  camera  image,  entering 
also  such  notes  as  may  be  of  value  for  the  development  of  the  plate  and  for  the  iconometric  plat- 
ting of  the  topography  recorded  upon  it  (by  the  action  of  the  light).  Having  made  sure  that  the 
cap  is  on  the  lens,  the  slide  is  withdrawn  from  the  plate  holder  and  the  plate  is  brought  into 
contact  with  the  frame  of  the  metal  box  by  turning  the  screw  G , figs.  84  and  85,  devised  for  this 
purpose.  The  surveyor  now  turns  the  camera  in  azimuth  until  the  lines  on  the  upper  face  of  the 
wooden  casing  show  that  it  is  properly  directed  or  oriented  to  include  the  panorama  section  to  be 
photographed  between  the  lines,  the  field  of  view  coinciding  with  the  outline  sketch  bearing  the 
number  of  the  plate  holder  in  the  camera.  Sighting  along  the  converging  lines,  shown  on  the 
side  face  of  the  wooden  camera  casing,  he  can  assure  himself  whether  the  view  on  the  image  plate 
reaches  high  or  low  enough.  If  it  does  not,  he  will  put  the  longer  dimension  of  the  camera 
upright,  unless  the  camera  was  already  in  that  position.  He  levels  carefully,  in  the  manner  pre- 
viously described,  aud  exposes  the  plate.  Whenever  the  sun  shines  inside  of  the  front  hood  it 
should  be  shaded  off  during  the  exposure  of  the  plate  by  holding  something  above  the  hood. 
Under  no  circumstances  should  the  sun  be  permitted  to  shine  upon  the  lens. 

Every  evening,  after  returning  to  the  survey  camp,  the  surveyor  replaces  the  exposed  plates 
in  his  dark  tent  by  new  ones,  using  a ruby-colored  light.  He  also  marks  the  exposed  plates  in 
one  corner,  before  removal  from  the  holder,  with  his  initials,  the  number  of  the  dozen  and  of  the 
plate  (the  same  number  as  given  to  the  corresponding  outline  sketch),  using  a soft  lead  pencil  for 
this  purpose;  e.  g.,  IV,  5,  means  plate  No.  5 of  the  fourth  dozen,  or  the  forty-first  plate.  The 
exposed  plates  are  now  placed  into  a double  tin  box,  fig.  93,  which  can  be  closed  hermetically,  and 
which  will  float  when  filled  with  two  dozen  plates,  should  the  same  be  accidentally  thrown  into 
6584 45 


706 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


water.  These  boxes  are  shipped  to  the  head  office  in  Ottawa,  where  the  plates  are  developed  by 
a specialist. 

The  data  obtained  with  the  aid  of  the  transit  for  triangulation  purposes  are  recorded  in  the 
field  book  in  the  usual  manner,  as  customary  for  such  work. 

The  horizontal  angles  observed  with  the  transit  (or  altazimuth  instrument)  to  the  points  of 
the  terrene  marked  on  the  outline  sketch  which  accompanies  each  negative,  serve  not  only  for  the 
orientation  of  the  horizontal  projection  of  the  plate  on  the  plan  (the  so-called  “picture  trace”), 
but  they  also  serve  to  counteract  in  a measure  and  to  ascertain  the  distortion  of  the  paper  prints 
(or  photographic  enlargements).  The  vertical  angles,  together  with  the  platted  distances,  are 
used  to  check  and  verify  the  position  of  the  horizon  line  on  the  different  photographs. 

The  most  important  camera  stations  are  occupied  by  the  surveyor;  the  secondary  stations  by 

the  assistant  surveyor,  with  his  own  camera.  No  trigono- 
metric observations  are  made  by  the  assistant  while  occupy- 
ing the  secondary  statious. 

All  views  are  taken  with  the  same  stop:  // 36. 

(4)  The  United  States  Coast  and  Geodetic  Survey  camera. — 
The  original  type  of  the  Coast  and  Geodetic  Survey  camera, 
used  in  connection  with  the  Alaskan  boundary  survey,  was 
similar  in  form  to  Deviile’s  original  camera,  except  that  it 
had  a special  tripod  with  ball  and  socket  adjustment  and 
that  the  teeth  which  serve  to  mark  the  principal  and  horizon 
lines  on  the  negative  could  be  turned  by  revolving  one  button 
to  be  pressed  into  contact  with  the  photographic  plate. 

This  camera  was  also  provided  with  a ground  glass, 
enabling  the  surveyor  to  inspect  the  entire  field  controlled  by 
each  plate  before  exposure,  and  giving  ready  means  for  test- 
ing the  positions  of  the  teeth  which  mark  the  horizon  line. 

The  camera  itself  was  a plain  rectangular  box  made  of 
well-seasoned  mahogany  (If  by  5g  by  inches  in  size,  and  it 
was  used  always  in  the  same  position,  with  the  short  faces 
vertical.  The  bamboo  tripod  legs  were  composed  of  three  pieces,  each  10  inches  long,  and  screwed 
together  at  the  joints.  When  dismembered  the  tripod  was  carried  in  a sole-leather  packing  case 
together  with  the  camera,  twelve  plates  (in  six  double  plate  holders),  notebook,  barometer,  thei- 
mometer,  yellow  color  screen,  etc. 

The  new  phototopographic  camera  of  the  Coast  and  Geodetic  Survey  is  a phototheodolite, 
resembling  Colonel  Laussedat’s  latest  pattern  which  will  be  described  in  the  following  pages. 

IV.  SURVEYING  CAMERAS  COMBINED  WITH  GEODETIC  INSTRUMENTS. 

(Phototheodolites,  photographic  plane  tables,  etc.) 

The  data  acquired  in  the  field  with  pliotogram meters  of  the  class  just  described  had  to  be 
supplemented  with  observations  made  in  the  field  with  some  geodetic  instrument  (transit,  plane 
table,  etc.)  in  order  to  obtain  complete  topographic  surveys  of  the  regions  traversed  by  the  photo- 
topographic  surveying  party. 

The  idea  of  combining  surveying  instruments  with  a photographic  camera  into  single  compact 
and  serviceable  instruments  originated  very  early  witli  phototopographic  workers,  and  refined 
photo  theodolites  and  photographic  plane  tables  are  to  this  day  the  favorite  phototopographic 
instruments  in  Europe,  whence  they  are  also  exported  to  other  countries. 

These  more  or  less  complicated  instruments  have  been  devised  to  secure  great  precision  in  the 
work  undertaken  with  them,  and  refined  methods  are  employed  for  the  field  observations,  for  the 
culling  of  data  from  the  photographic  perspectives,  and  for  the  computations  made  in  the  oflice  to 
increase  the  general  precision  of  data  derived  from  the  operations  executed  in  the  field. 

Generally  speaking,  the  best  results  for  topographic  purposes  are  obtained  by  means  of 
photography,  if  we  bear  in  mind  that  phototopography  essentially  and  primarily  is  a constructive 
and  graphic  art,  based  upon  graphic  or  pictorial  records  (which  are  nothing  more  than  central 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


707 


projections  in  vertical  plan  of  objects  and  their  dimensions,  that  are  to  be  transposed  graphically 
into  orthogonal  projections  into  horizontal  plan).  Instrumental  observations  being  required  only 
to  furnish  such  elements  as  may  be  needed  to  make  the  graphic  transpositions  (iconometric  platting 
in  a reduced  scale)  of  the  lines  of  directions  and  distances,  and  also  to  obtain  checks  or  a proper 
control  for  the  work  in  its  entirety. 

Photographic  surveys  have  been  conducted  principally  in  regions  where  other  surveying 


^ ' g 9 V 

methods  are  either  precluded  or  where  their  application  would  entail  great  cost  and  consume  too 
much  time,  and  such  regions  are  characterized  chiefly  by  a rugged  and  broken  topography. 

The  necessity,  therefore,  lies  close  at  hand  to  devise  instruments  that  will  not  readily  get  out 
of  adjustment  or  drop  to  pieces  when  transported  over  rugged  mountain  trails,  and  the  more 
simplified  their  structural  composition  the  more  available  will  they  become  for  the  production  of 
rapid  and  accurate  work. 

It  is  at  once  evident  that  the  combination  of  a camera  and  a surveying  instrument  into  a well 
united,  well-balanced,  easily  manipulated,  and  essentially  light  and  withal  rigid  instrument  is  not 
easily  accomplished.  It  is  not  surprising  therefore,  when  searching  the  published  descriptions  of 


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UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


phototheodolites  and  other  photogramiueters,  to  come  upon  a great  number  of  types  in  which  the 
many  difficulties  have  been  overcome,  more  or  less  successfully,  by  various  devices. 

We  may  find:  A large-sized  theodolite  with  a small  camera,  placed  centrally  between  the  Y 
supports,  after  removal  of  the  telescope  from  the  latter,  both  being  interchangeable; 

A large  camera  mounted  upon  the  horizontal  circle  with  a telescope  and  vertical  circle  attached 
eccentrically  (at  either  side  of  the  camera); 

A large  eeutrically  located  camera,  the  lens  of  which  serves  at  the  same  time  as  objective  of 

the  telescope,  the  correspond- 
ing eyepiece  being  at  the  cen- 
ter of  the  frame  that  ordinarily 
supports  the  ground  glass 
plate  (in  this  form  the  camera 
itself  is  the  telescope); 

Instruments  where  the 
board  of  the  plane  table  has 
been  replaced  by  a surveying 
camera,  the  upper  face  of 
which  receives  and  supports 
the  plane-table  sheet  and 
plane-table  alidade;  also  var- 
ious other  combinations  (some 
with  compass  attachments). 

This  class  of  instruments 
has  been  in  use  for  large  scale 
surveys  and  where  the  instru- 
mental outfit  could  readily  be 
brought  very  near  the  stations 
to  be  occupied  by  convenient 
means  of  transportation,  the 
instruments  rarely  being  sub- 
jected to  such  primitive  and 
rough  methods  of  transporta- 
tion over  long  distances,  as  it 
generally  has  been  the  case  on 
our  continent  when  surveying 
cameras  have  been  used. 

(1)  The  new  Italian  photo- 
tlieodolite , devised  by  L.  P. 
Paganini.  — Pagauini’s  model 
of  1884  has  been  described  in 
Appendix  No.  3,  United  States 
Coast  and  Geodetic  Survey 
Report  for  1S93. 

The  following  description 
of  Paganini’s  new  phototheod- 
olite, model  of  1890,  has  been  extracted  from  L.  P.  Paganini’s  “Nuovi  appunti  di  fototopografia,” 
Roma,  1891: 

The  general  form  and  the  dimensions  of  the  camera  box  of  Paganini’s  new  phototheodolite 
remain  about  the  same  as  with  the  older  model,  the  principal  change  resting  in  the  omission  of 
the  eccentric  telescope  which  has  been  replaced  by  the  centrally  mounted  camera,  which  may,  at 
will  of  the  observer,  be  converted  into  a telescope. 

The  telescopes  which  we  generally  find  attached  to  surveying  instruments  consist  of  a tube, 
slightly  conical  in  shape,  having  a positive  lens  or  a system  of  convergent  lenses  at  one  end  (the 
“objective”)  which  produce  within  the  telescope  a real  and  inverted  image — the  same  as  the 
camera  lens — of  any  object  toward  which  the  lens  may  be  directed.  The  other,  smaller  end  of 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


709 


One  liair  is  vertical  and  the 


the  telescope  tube,  has  a still  smaller  tube  inserted  into  it  which  may  be  moved  in  the  direction 
of  the  axis  of  the  tube.  This  second  tube  also  contains  a system  of  convergent  lenses — so-called 
“ocular  lens”  or  “eyepiece”  of  the  telescope— which  serve  to  project  an  enlargement  of  the 
image  in  the  telescope  upon  the  retina  of  the  observer’s  eye.  In  the  image  plane  of  the  objective 
(within  the  telescope),  is  the  so-called  diaphragm — a ring-shaped  metal  disk — to  one  side  of  which 
a pair  of  cross  hairs — spider  webs,  cocoon  threads,  or  lines  cut  into  a thin  piece  of  plate  glass — is 
attached  in  such  a way  that  the  hairs  fall  within  the  image  plane, 
other  horizontal,  their  point  of  intersection  coincid- 
ing with  the  optical  axis  of  the  telescope. 

The  old  camera  was  provided  with  the  objective, 
and  a corresponding  eyepiece  had  only  to  be  added 
to  convert  the  camera  into  a surveying  telescope. 

In  the  instrument  under  consideration  the  eyepiece 
consists  of  a positive  lens  set,  known  in  optics  as 
“Ramsden’s  ocular  lens.”  The  inner  wall  surfaces 
of  the  camera  box  should  be  well  blackened  to  avoid 
any  side  reflection  and  a consequent  dimness  in  the 
appearance  of  the  cross  wires. 

The  camera  proper  consists  of  two  parts,  a trun- 
cated pyramid  A , tigs.  94  to  98,  and  a cylindrical 
attachment  B,  into  which  the  tube  t is  inserted. 

A second  tube  within  the  cylinder  t may  be 
moved  in  the  direction  of  the  optical  axis  by  means 
of  a screw,  the  threads  of  which  have  a rise  of  one 
millimetre.  By  revolving  the  inner  tube  the  lens  is 
brought  nearer  to  or  farther  from  the  image  plane, 
the  lens  remaining  parallel  with  the  image  plane  at 
any  position  that  may  thus  be  given  to  the  lens. 

A scale  a,  ligs.  94  and  98,  graduated  to  millime- 
tres, is  permanently  attached  to  the  tube  t and  it  lies 
very  close  to  the  ring  n,  the  circumference  of  which 
is  divided  into  ten  equal  parts.  (This  graduated 
ring  n is  soldered  upon  the  cylinder  u containingthe 
camera  lens.)  This  scale  a (extending  in  a direction 
parallel  to  the  optical  axis  of  the  lens)  has  a mark, 
coinciding  with  the  index  rim  of  the  ring  n,  thus 
indicating  the  focal  length  of  the  camera  lens  when 
focused  upon  objects  at  infinite  distance.  The  milli- 
metre graduation  of  the  scale  a , extending  from  the 
zero  mark  in  the  direction  toward  the  ground  glass 
serves  to  ascertain  the  focal  lengths  for  objects 
nearer  the  camera  station.  The  circumferential 
graduation  on  the  ring  n serves  to  read  one-tenth 
of  one  revolution  of  the  tube  »,  which  is  equal  to 
an  axial  motion  of  the  lens  of  0T  millimetre,  hence 
the  focal  length  for  any  object  focused  upon  may 
be  read  to  single  millimetres  on  the  scale  a and  to 
tenths  of  a millimetre  on  the  graduated  ring  n. 

The  construction  of  this  phototheodolite  is 
such  that  the  optical  axis  of  the  camera  lens  is 
glways  at  right  angles  to  the  picture  plane — the  ground-glass  surface  or  the  sensitive  film  of  the 
photographic  plate.  1 he  intersection  of  the  optical  axis  and  the  picture  plane,  the  principal 
point,  is  marked  by  the  intersection  P,  lig.  9/,  of  the  two  very  fine  platinum  wires  0 O'  and  / /v, 
one  horizontal  and  the  other  vertical  when  the  instrument  is  in  adjustment.  These  wires  are 
stretched  across  the  back  ot  the  camera,  box  as  close  as  possible  to  the  picture  plane.  The 
buttons  5,  figs.  94  and  95,  serve  to  give  tension  to  the  wires.  The  wire  0 O'  corresponds  to  the 
horizon  line  and  the  vertical  wire  J J ' corresponds  to  the  principal  line  of  the  perspective  repre- 
sented by  the  image  on  the  ground-glass  plate. 


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UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


Fig.  9G  shows  the  rear  view  of  this  instrument,  the  ground  glass  having  been  replaced  by  an 
opaque  plate,  strengthened  by  a metal  frame  and  ribs,  which  supports  the  Ramsden  eyepiece  in 
the  center,  its  optical  axis  coinciding  with  that  of  the  camera  lens.  The  cross  wires  0 O',  f f , at 
the  rear  of  the  camera,  serve  also  for  the  astronomical  telescope  into  which  the  camera  may  be 
converted  by  attaching  the  opaque  plate  with  central  eyepiece  as  shown  in  fig.  (JG.  The  tittiug  of 
this  eyepiece  allows  for  axial  motion  to  adjust  its  position  to  avoid  parallax. 

The  rear  opaque  plate  and  the  other  sides  of  the  camera  box 
are  made  of  cardboard  (impregnated  with  chemicals  to  render  it 
impervious  to  moisture),  and  they  are  stiffened  by  frames  and  ribs 
of  metal  as  illustrated  in  figs.  94  and  9G. 

The  cylindrical  part  B , figs.  94,  95,  and  97,  is  inclosed  by  a solid 
metal  collar  C,  which  is  held  in  position  within  the  metal  ring  1 11 
by  four  screws  R,  R' , S,  S'.  This  ring  l V is  connected  with  the 
frame  g g'  by  means  of  two  arms  l g and  l'  g',  all  being  cast  into  one 
piece.  The  frame  g g1  has  pivots  q attached  to  it  which  form  the 
horizontal  axis  of  rotation  for  the  camera. 

This  instrument  is  provided  with  a vertical  circle,  fig.  94,  hori- 
zontal circle  H , figs.  94, 

95,  and  98,  verniers, 

reading  microscopes,  ^**^7 

levels  L , figs.  94  and  R 

9G,  clamps,  and  slow-  8 t c 

motion  screws,  forming  a complete  transit  with  cen- 
trally mounted  “camera-telescope.” 

Fig.  98  represents  a vertical  section  of  this  in- 
strument. The  scale  a,  already  described,  is  here 
placed  on  top  of  the  tube  u to  illustrate  its  function 
better,  yy  = uprights,  supporting  the  horizontal 
axis  of  rotation  of  the  “camera- telescope.”  li  = ali- 
dade supplied  with  verniers.  H = lower  limb  or 
horizontal  circle  bearing  the  graduation;  it  is  sup- 
ported on  the  tripod  head  Tby  three  leveling  screws 
W.  a = casing  for  conical  center,  q1  = central 
clamp-screw,  firmly  uniting  T and  H (it  guards 
against  an  accidental  falling  off  of  the  instrument 
from  the  tripod);  it  screws  into  a ball  which  is  sup- 
ported by  the  hemispherical  socket  w of  the  lower 
part  of  a. 

The  horizontal  circle  has  a diameter  of  40-5  cen- 
timetres. It  is  graduated  into  thirty  minutes,  and  its 
verniers  read  to  single  minutes. 

The  photographic  plates  are  48  by  24  centimetres, 
the  same  size  as  for  the  1884  model  camera. 

The  objective  lens  was  an  aplanat  of  Steinheil  of 
237’7  millimetres  focal  length.  More  recently,  how- 
ever, the  Italian  phototheodolites  have  been  provided 
with  anastigmats  of  Zeiss. 

The  column  E,  figs.  94,  95,  96,  and  98,  forming  a 
prolongation  of  the  lower  arm  V g1,  is  held  in  place 
by  two  counter  screws  m and  m',  fig.  9G,  which  serve 
to  hold  the  horizontal  axis  of  rotation  of  the  camei  a in  a fixed  position,  avoiding  accidental  changes 
during  the  execution  of  a set  of  panorama  pictures. 

After  unscrewing  the  nuts  (V , fig.  98,  the  tripod  legs  may  be  removed.  They  serve  as 
“alpenstocks”  when  the  instrument  is  being  transported  from  station  to  station.  The  camera- 
telescope  is  lifted  out  of  the  wyes  and  packed  in  a separate  case ; the  lower  part  of  the  instrument 
is  packed  in  another  case,  and  the  plate  holders  and  plates  are  transported  in  a third  case. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


711 


(2)  Pliolofirammetric  theodolite  of  Prof.  S.  Finsterw alder. — This  phototheodolite  (manufac- 
tured by  Max  Ott  (A.  Ott),  of  Kemp  ten,  in  Bavaria)  was  devised  by  Dr.  Finsterwalder  after 
many  years  of  practical  work  and  experience  incidental  to  his  Alpine  surveys  and  studies  of 
glacial  motion.  This  experience  taught  him  the  desirability  of  producing  a camera  compactly 
built,  rigidly  constructed  in  all  its  parts,  and  yet  having  a minimum  of  weight.  To  avoid  the 
extra  weight  when  transporting  a separate  theodolite  (with  the  surveying  camera)  for  the  trigono- 
metric location  of  the  stations  occupied  with  the  camera,  he  provided  the  surveying  camera  with 
the  means  for  observing  horizontal  and  vertical  angles. 

Professor  Fiusterwalder’s  phototheodolite  is  illustrated  in  tig.  99.  The  entire  outfit  weighs  10 
kilogrammes,  which  weight  is  distributed  as  follows: 


Kilogrammes. 

The  instrument  per  se 2 7 

Carrying  case  tor  same 24 

The  tripod  1‘7 

One  dozen  leather  plate  holders,  including 

the  twelve  plates 2 5 

Packing  case  for  the  latter 07 


Professor  Finsterwalder  has  used  a double  ana- 
stigmat  of  Gorz  and  later  an  anastigmat  of  Zeiss,  with 
a constant  focal  length  of  150  millimetres.  With  this 
focus  the  lens  will  photograph  perspectively  correct  a 
plate  of  160  by  200  millimetres.  The  plates  have  a size 
of  120  by  160  millimetres  and  they  command  an  effect- 
ive horizontal  field  of  53°,  enabling  the  observer  to 
cover  the  complete  panorama  with  seven  plates. 

For  the  central  or  normal  position  of  the  objective 
the  camera  commands  an  effective  vertical  field  of  ± 20°. 
This  range  would  often  be  insufficient,  particularly 
when  photographing  mountainous  terrene  of  an  alpine 
character,  therefore  it  was  deemed  advisable  to  mount 
the  objective  on  a slide,  which  will  permit  a consider- 
able change  in  the  vertical  sense.  Owing  to  this  de- 
vice, objects  subtending  an  angle  of  depression  of  35°, 
together  with  others  subtending  an  angle  of  elevation 
of  5°,  may  still  be  photographed  on  the  same  plate, 
giving  a vertical  control  of  40°  in  all. 

In  extreme  cases,  when  it  should  become  desirable 
to  photograph  objects  subtending  angles  of  -f-  35°  and 
of  —35°,  or  70°  in  all,  Professor  Finsterwalder  recom- 
mends the  exposure  of  two  plates  in  succession,  com- 
manding the  same  (identical)  horizontal  angle,  exposing 
one  with  the  maximum  elevation  of  the  objective  slide 
and  the  other  with  the  maximum  depression  of  the  lens. 
Thus,  inclined  pictures  are  not  only  avoided,  but  the 
effective  surface  of  the  plate  is  utilized  to  the  best 
advantage,  and  the  weight  of  glass  to  be  carried  is 
reduced  to  the  minimum. 

In  order  to  obtain  uniformly  accurate  results  with 
the  relatively  short  focal  length  (maintaining  a constant 
distance  between  the  lens  and  the  sensitive  surface  of 


the  plates),  the  plates  are  not  inserted  into  plate  holders  (where  the  variable  thickness  of  the  glass 
would  affect  the  so-called  “constant  focal  length”),  but  they  are  pressed  directly  against  a metal 
frame,  which  forms  the  back  ot  the  camera  box,  very  similar  to  the  arrangement  described  for  Cap- 
tain Devi  lie’s  (Canadian)  camera.  To  do  this,  use  has  been  made  of  Dr.  Neuhauss’s  leather  plate 
holders,  formed  like  a sack  If  fig.  99.  The  inner  edges  of  the  metal  frame  are  graduated  in  order 
to  locate  the  principal  and  horizon  lines  upon  the  negatives. 


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UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


These  leather  sacks  have  metal  slat  arrangements,  and  the  transfer  of  the  plate  from  the  sack 
to  the  camera  is  made  by  hooking  the  sack  with  its  mouth  to  the  upper  edge  of  the  rear  camera 
side.  While  holding  the  bag  in  a vertical  position  the  slats  are  opened  and  the  plate  is  allowed 
to  slide  from  the  sack  into  the  carrier  to  be  exposed. 

Springs  are  provided  at  the  back  of  the  camera  box  to  check  against  a sudden  dropping  of 
the  plate  into  the  metal  carrier,  to  avoid  a breaking  or  cracking  of  the  plate  by  striking  the  closed 
lower  metal  slide  of  the  plate  carrier  too  hard.  These  springs  also  serve  to  press  the  plate,  when 
in  position  for  exposure  in  the  carrier,  into  perfect  contact  with  the  graduated  metal  frame  at  the 
back  of  the  camera  box. 

By  withdrawing  the  upper  curved  handle,  fig.  99,  at  the  back  of  the  camera,  the  tension  of 
the  springs  may  be  reduced  and  the  plate  glides  into  position  to  be  exposed.  After  exposure  the 
lower  slide  is  withdrawn  and  the  plate  will  slip  into  the  empty  sack  B , which  had  been  hooked  to 
the  lower  edge  of  the  camera  back  for  this  purpose,  as  illustrated  in  fig.  99. 

The  eccentricity  of  the  center  of  gravity,  by  applying  the  weight  of  the  sack  and  plate  to  one 
side  of  the  camera,  does  not  affect  the  adjustments  of  the  instrument  sufficiently  to  throw  the 
photographic  plate  out  of  the  vertical  plane  in  which  the  exposure  should  be  made.  This  camera 
theodolite  is  accurately  balanced  when  no  sack  is  attached,  in  which  form  it  is  used  to  measure 
the  angles  that  may  be  needed  to  locate  the  camera  station  (geographically,  and  also  in  the 
vertical  sense)  with  reference  to  surrounding  trigonometric  signals. 

In  order  to  convert  this  camera  into  a theodolite  (with  centrally  located  telescope),  the  back 
of  the  camera  is  provided  with  a telescopic  eyepiece  E,  of  a magnifying  power  of  from  7 to  8. 
This  eyepiece  is  adjusted  to  form  a surveying  telescope  with  the  camera  lens  0 as  objective.  It 
is  provided  with  cross  wires  or  webs,  and  a shutter  affords  the  means  to  shut  out  the  light  when 
the  instrument  is  used  for  photographing. 

The  camera  lens  (objective  of  “camera  telescope”)  being  movable  in  the  vertical  sense  within 
a range  of  100  millimetres,  all  objects  falling  within  a range  of  =t  17°  may  be  bisected  with  this 
telescope.  The  definition  of  points  to  be  bisected,  when  above  or  below  the  camera  horizon, 
would  be  very  poor  if  the  eyepiece  E were  rigidly  fixed  in  the  horizontal  position,  but  by  means 
of  the  metal  arms-AA  the  eyepiece  may  be  revolved  about  a horizontal  axis  in  such  a way  that  it 
will  always  be  directed  to  the  center  of  the  camera  lens. 

With  the  double  anastigmat  of  Gorz,  which  produces  a perfectly  flat  picture  (with  neither 
spherical,  chromatic,  nor  astigmatic  aberration  or  distortion),  a change  in  the  focus  of  the  eyepiece 
will  rarely  be  required. 

Horizontal  angles  may  be  observed  directly  by  means  of  a horizontal  circle  of  120  millimetres 
diameter,  which  is  provided  with  two  verniers  reading  to  single  minutes.  A series  of  experimen- 
tal tests  has  proven  that  horizontal  angles  observed  between  points  of  considerable  difference  in 
altitude  may  be  obtained  within  a limit  of  error  of  0-4'.  This  instrument,  therefore,  gives  results 
sufficiently  accurate  to  locate  the  camera  station  trigonometrically  with  reference  to  surrounding 
fixed  points  of  known  positions,  if  they  are  not  too  far  distant  to  be  defined  with  this  low-power 
telescope. 

Vertical  angles,  however,  can  not  be  obtained  directly.  Still,  by  means  of  a scale  and  vernier 
attached  to  the  camera-lens  slide  (or  front  board)  the  change  of  the  camera  lens  from  its  central 
or  normal  position  (that  is,  a value  directly  proportional  to  the  tangent  of  the  vertical  angle)  may 
be  read  to  <>05  millimetre.  The  slide  motion  of  the  front  board  is  accomplished  with  a rack  and 
pinion,  and  experience  has  proven  that  the  observations  may  be  obtained  within  a limit  of  error 
(converted  into  arc  measure)  of  1 minute. 

The  three  rods,  designated  by  h in  fig.  99,  are  each  100  millimetres  long.  They  serve  to 
elevate  the  instrument  support  and  the  three  leveling  screws  8 sufficiently  high  above  the  tripod 
to  allow  full  play  for  the  leather  plate  holders  B , when  they  are  placed  in  position  to  receive  the 
exposed  plate.  The  tripod  legs  may  be  folded  together  to  one-half  their  length. 

No  ground-glass  plate  being  provided,  a special  finder  has  been  devised  correctly  showing  the 
field  controlled  by  the  plate  for  any  position  of  the  camera  lens.  (See  Zeitsclirift  fiir  Instru- 
mentenkunde,  October,  1895.) 

(3)  Photo-theodolite  for  precise  worh , by  O.  Ney. — 1 This  instrument  has  been  patented  in  the 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


713 


German  Empire,  and  the  following  description  has  been  taken  from  Zeitschrift  fiir  Instrumenten- 
kuude,  page  55,  1895: 

In  the  construction  of  this  instrument,  figs.  100  and  101,  it  has  been  sought  to  satisfy  the 
following  requirements: 

First.  The  camera  should  be  sufficiently  large  to  produce  clear  and  well-defined  perspectives. 

Second.  The  general  disposition  of  weight  and  mass  should  be  symmetrical  (the  camera  and 
the  telescope  of  the  theodolite  were  to  be  mounted  centrally). 

Third.  The  weight  of  the  instrument  should  be  reduced  to  the  minimum  consistent  with 
rigidity  and  sufficient  strength  to  assure  a free  and  easy  manipulation,  as  well  as  durability  or 
permanency  of  its  adjustments  when  used  in  the  field. 

This  instrument  is  composed  of  two  distinct  parts,  the  camera  proper  (with  horizontal  circle) 


between  camera  and  transit  is  readily  accomplished  (both  being  centered  over  the  same  instru- 
ment support)  with  accuracy  and  expediency. 

The  principal  advantages  attached  to  this  disposition  of  the  component  parts  of  the  photo- 
theodolite may  be  cited  as  follows: 

First.  The  symmetrical  and  central  mounting  of  the  camera  and  transit  telescope  insures 
accuracy  in  the  results. 

Second.  The  weight  of  each  separate  instrument — camera  and  transit — has  been  reduced  to 
a minimum. 

Third.  A disturbance  of  the  adjustments  of  the  instrument  support  (including  tripod)  may 
be  completely  avoided  by  having  the  plate  inserted  and  the  slide  withdrawn  before  placing  the 
camera  box  into  position  upon  the  upper  alidade  limb. 

The  carrying  into  effect  of  the  ideas  just  mentioned  has  been  greatly  aided  by  supplying  all 


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UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


leveling  and  clamp  screws  with  spherical  ends  resting  upon  plates  in  such  a manner  that  a free 
play  of  motion  will  take  place.  These  spherical  terminations  of  the  screws  were  originally  devised 
by  Reich  el. 

The  two  forms  in  which  this  instrument  may  be  used  are  shown  in  figs.  100  and  101.  The 
former  shows  the  photo-topographic  camera  (simdar  to  Professor  Finsterwalder’s  instrument),  and 
the  latter  shows  the  transit  with  compass  B. 

1 ) is  the  very  rigid,  yet  essentially  light,  instrument  support,  the  three  arms  being  cast  into 
one  piece  with  the  bearing  for  the  conical  pivot  attached  to  the  horizontal  limb  T. 

T is  the  lower  graduated  limb  and  A is  the  upper  limb  of  the  alidade  bearing  the  verniers. 

A large  circular  level  is  attached  to  the  center  of  the  upper  limb  of  the  alidade.  The  latter 
has  three  hardened  plates  inserted  into  its  upper  surface  (at  S,  figs.  100  and  101),  one  with  a plane 
surface,  the  second  with  a conical  cavity,  and  the  third  with  a v-shaped  groove  or  slot.  They  form 
the  supports  for  the  spherical  terminations  of  the  three  screws  K,  fig.  100,  attached  to  either  the 
transit  or  the  surveying  camera.  These  screws  are  received  between  the  flanges  C that  form  a 
part  of  the  base  ring  supporting  either  the  camera  or  the  telescope  wyes  if,  fig.  101. 

The  two  sets  of  three  screws  K (one  for  camera  and  one  set  for  the  transit)  serve  to  adjust 
the  horizon  lines  of  both  instruments  and  to  bring  them  into  the  same  horizontal  plane. 

The  transit  telescope  is  arranged  for  stadia  reading  (after  Porro’s  method),  with  100  as  the 
constant  factor.  The  telescope  level  reads  to  20",  and  the  final  adjustment  of  the  transit  is 
accomplished  by  means  of  this  level.  The  striding  compass  B,  fig.  101,  is  graduated  to  read  to 
30',  whereas  the  horizontal  circle  reads  either  to  10"  or  20",  according  to  the  size  of  the  instrument. 

In  order  to  secure  the  transit  and  the  camera  to  the  horizontal  circle  (which  both  have  in 
common)  three  horseshoe-shaped  clasps  (shown  near  C,  figs.  100  and  101)  are  hinged  to  the  upper 
limb  A of  the  alidade  in  such  a way  that  they  straddle  either  set  of  the  three  screws  K of  the 
projecting  flanges  C (when  they  are  turned  up  as  shown  in  the  figs.  100  and  101). 

Each  of  these  clasps  has  a clamp  screw  with  lever  handle  B,  fig.  101,  and  by  tightening  these 
three  clamp  screws  they  are  brought  to  bear  upon  the  hardened  heads  of  the  screws  Ji,  making 
a firm  connection  between  the  upper  limb  of  the  alidade  and  the  superimposed  transit  or  camera. 
This  connection  is  easily  made,  and  it  does  not  disturb  the  adjustments  of  the  instrument. 

This  instrument  is  made  in  two  sizes;  one  has  plates  13  by  18  centimetres,  and  the  other  18 
by  24  centimetres.  To  avoid  changes  in  the  dimensions  of  the  camera  box,  due  to  hygroscopic 
influences  of  the  atmosphere,  the  box  is  constructed  entirely  of  aluminium.  The  plate  holders  and 
the  movable  plate  carrier,  however,  are  made  of  mahogany,  impregnated  with  chemicals  to  make 
the  wood  impervious  against  moisture. 

To  avoid  any  possible  change  in  the  constant  focal  length,  due  to  an  uneven  thickness  of 
photographic  plates  or  of  the  plate  holders,  the  movable  carrier  may  be  moved  toward  the 
camera  lens  by  means  of  the  levers  L,  fig.  100,  until  the  sensitive  surface  of  the  photographic 
plate  is  brought  into  contact  with  a metal  frame,  securely  fastened  to  the  sides  of  the  camera  box, 
and  which  has  a centimetre  graduation  filed  into  its  inner  edges.  The  distance  of  the  rear  surface 
of  the  graduated  frame  from  the  second  nodal  point  of  the  camera  lens  constitutes  the  constant 
focal  length  of  the  camera. 

The  centimetre  graduation  on  the  inner  edges  of  the  metal  frame,  reproduced  on  the  margin 
of  the  negatives,  serves  to  ascertain  whether  the  sensitive  films  (or  the  contact  prints)  have  under- 
gone any  change  during  the  process  of  development  and  also  to  ascertain  the  amount  of  correction 
to  be  applied  to  the  perspective,  if  found  to  be  distorted,  before  using  it  for  the  iconometric 
platting. 

The  camera  is  provided  with  a pair  of  cross  levels  to  enable  the  observer  to  detect  any  change 
in  its  adjustments  prior  to  exposing  a plate.  These  levels  are  graduated  to  read  to  20"  of  arc. 
When  the  instrument  is  in  perfect  adjustment,  the  picture  plane  will  be  in  a vertical  plane  and 
the  principal  ray  will  be  in  the  same  horizontal  plane  as  the  optical  axis  of  the  telescope  (when 
level),  if  the  camera  were  replaced  by  the  transit  without  disturbing  the  tripod’s  position. 

When  this  camera  theodolite  is  adjusted,  the  vernier  M,  fig.  100,  will  read  zero  for  the  normal 
position  of  the  lens.  Still,  the  objective  may  be  elevated  or  depressed  by  35  millimetres,  which 
change  from  the  normal  or  central  position  of  the  lens  may  be  read  correctly  within  0.1  millimetre 


REPORT  FOR  1897 — PART  II.  APPENDIX  NO.  10. 


715 


on  the  scale  and  vernier  M,  fig.  100.  The  pneumatic  camera  shutter  is  arranged  both  for  time  and 
for  instantaneous  exposures,  a special  device  guarding  against  the  possibility  of  exposing  a plate 
before  it  is  brought  into  perfect  contact  with  the  graduated  metal  frame,  previously  mentioned. 

The  plate  holder  can  not  be  withdrawn  from  the  camera  before  the  slide  has  been  replaced, 
nor  as  long  as  the  plate  is  in  contact  witli  the  gradu- 
ated frame. 

(4)  The • phototlieodolite  of  Dr.  C.  Koppe. — Dr.  G. 

Koppe,  professor  at  the  Technical  High  School  in 
Braunschweig,  Germany,  is  an  ardent  advocate  of  pho- 
togrammetry  and  he  has  done  much  toward  populariz- 
ing  photographic  surveying  in  Germany.  His  work 
on  photogrammetry,  published  in  18S9,  is  an  excellent 
manual  both  in  respect  to  theory  and  practice,  in 
1S9C>  he  published  a treatise  on  photogrammetry  applied 
to  cloud  photography  for  meteorological  research. 

This  phototheodolite,  fig.  102,  has  a centrally 
mounted  camera  with  the  telescope  on  one  side  and 
the  vertical  circle  on  the  other.  The  horizontal  axis 
between  the  two  wyes  has  been  widened  into  a conical 
ring  R,  into  which  the  camera  C may  be  inserted.  Four 
stout  springs /press  the  camera  C tightly  against  the 
ring  surface  forming  the  base  of  the  conical  ring  R. 

After  insertion  into  the  ring,  the  camera  C is  revolved 
within  the  former  until  the  end  of  the  screw  h abuts 
against  the  stop  d,  when  the  horizon  line  of  the  per- 
spective (negative)  should  be  horizontal. 

The  camera  axis  is  parallel  with  the  optical  axis 
of  the  telescope  T,  both  axes  being  in  the  same  horizontal  plane  when  the  vernier  of  the  vertical 
circle  reads  zero.  When  elevating  or  depressing  the  telescope  T the  camera  axis  will  follow  the 

same  motion,  both  remaining 
parallel.  The  instrument  will 
be  in  equilibrium  with  the  cam- 
era de-  or  attached.  The  hori- 
zontal axis  of  this  instrument 
may  be  adjusted  by  means  of 
the  striding  level  A,  which, 
when  necessary,  may  be  re- 
placed by  a striding  compass 
in  a manner  similar  to  that 


illustrated  in  fig.  101. 

Since  the  telescope  may  be 
reversed  in  the  wyes,  an  error 
of  collimation  and  any  index 
error  of  the  vertical  circle  may 
be  found  or  eliminated. 

There  are  neither  slides 
nor  plate  holders  provided  with 
this  instrument,  the  plates  be- 
ing inse  ted  directly  into  the 
camera.  This  may  be  done  in 

the  field  by  aid  of  the  packing  case  specially  constructed  to  serve  as  a dark  chamber,  fig.  103. 

I his  case  is  made  ol  wood  with  double  doors,  each  door  having  a circular  hole  A,  which 
is  filled  in  v ith  a flexible,  light  tight,  and  dark-colored  material,  forming  sleeves  in  such  a way 
that  the  hands  of  the  operator  may  be  thrust  through  an  elastic  opening  in  the  center  (of  the 


716 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


circular  openings).  The  fabric  will  close  tightly  around  the  wrists — when  the  interior  of  the  case 
will  be  perfectly  dark — and  the  sleeves  A will  permit  free  play  to  the  hands  for  manipulating  the 
camera  and  plates  within  the  space  L of  the  case. 

This  case  is  inclosed  with  a tight-fitting  sole-leather  covering,  having  two  flaps  S to  protect 
the  openings  A against  the  admission  of  dust  when  the  packing  case  is  transported  on  the  back 
of  the  instrument  bearer. 

The  entire  instrument,  except  the  tripod,  may  be  packed  into  this  case  for  transportation.  It 
also  contains  two  boxes,  Kv  and  7l2;  the  former  receives  the  exposed  plates  (negatives)  while  the 
latter  contains  the  supply  of  unexposed  plates. 

When  a plate  is  to  be  exchanged  the  camera  C is  placed  into  the  packing  case  and  both  doors 
as  well  as  the  leather  main  flap  or  cover  are  securely  closed;  both  hands  are  now  inserted  through 
A,  and  after  the  sleeves  are  tightly  closed  about  the  wrists  the  camera  is  opened,  the  exposed 
plate  removed  and  placed  into  the  box  Kx  (as  shown  at  P,  fig.  103).  The  door  T is  closed  and  a 
new  plate,  taken  from  the  box  K2 , is  placed  into  the  camera  (as  shown  by  y,  fig.  103)  and  the 
camera  back  is  closed,  when  the  camera  will  be  ready  for  another  exposure. 

The  constant  focal  length  of  this  camera  is  represented  by  the  distance  between  the  second 
nodal  point  of  the  lens  aud  the  rear  surface  of  a metal  frame  (similar  to  that  of  Rey’s  photo- 
theodolite) permanently  attached  to  the  rear  of  the  camera  box. 

The  inner  edges  of  this  metal  diaphragm  or  frame  are  graduated  into  centimetres;  the  middle 

graduation  marks  of  the  horizontal  sides  of  the  frame  locate  the 
principal  line,  while  the  middle  graduation  marks  of  the  vertical 
sides  represent  the  termini  of  the  horizontal  line  on  the  perspec- 
tives. The  focal  length,  once  determined,  will  remain  unchanged 
for  all  plates. 

This  instrument  has  been  manufactured  for  Professor  Koppe 
by  F.  Randhagen,  in  Hanover,  Germany. 

The  “Topographic  Bureau”  of  the  Swiss  Republic  has  used 
a phototheodolite  constructed  after  the  model  of  Dr.  Koppe’s  in- 
strument. The  experience  in  Switzerland,  however,  seems  to 
have  decided  the  topographic  bureau  not  to  replace  the  plane 
table  by  the  phototheodolite  for  general  topographic  surveys 
executed  by  that  bureau. 

(5)  Phototheodolite  devised  by  F.  Pollack , manufactured  by  R. 
Lechner  in  Vienna , Austria. — With  this  instrument  (fig.  104)  the 
camera  C is  centrally  located,  and  it  rests  upon  a horizontal  circle.  The  telescope  F and  the 
vertical  circle  are  mounted  at  one  side  of  the  camera,  a weight  G counterbalancing  both  on  the 
other  side  of  the  camera. 

Aluminum  has  been  used  very  freely  in  the  construction  of  this  phototheodolite  in  order  to 
reduce  the  weight  as  low  as  possible.  This  instrument  has  been  manufactured  in  two  sizes;  the 
horizontal  circle  of  the  small  sized  one  is  graduated  to  30',  the  verniers  reading  F,  while  the  larger 
one  has  a circle  graduated  to  20',  and  its  verniers  read  20".  The  telescope  F is  mounted  similarly 
to  that  of  the  so  called  Danish  plane  table  alidade. 

The  adjustment  of  the  horizontal  axis  of  revolution  of  the  telescope  F is  accomplished  by 
means  of  a special  level.  Clamps  and  slow  motion  screws  are  provided  for  both  the  horizontal 
and  vertical  circles.  The  telescope  has  a focal  length  of  27  centimetres  and  an  opening  of  31 
millimetres,  with  a magnifying  power  of  9 to  18  diameters.  The  telescope  is  arranged  for  stadia 
reading,  and  it  has  100  as  the  constant  multiplier.  The  telescope  level  L is  graduated  to  10"  or 
20".  The  vertical  circle  is  graduated  to  20'  and  its  two  verniers  read  to  20".  , 

The  camera  box  is  made  of  aluminum  and  it  is  provided  with  a Zeiss  anastigmat.  By  means 
of  the  rack  and  pinion  2 the  lens  may  be  elevated  or  depressed  by  either  30  or  50  millimetres, 
according  to  the  size  of  the  instrument.  The  scale  f,  with  vernier  n,  serves  to  measure  the  vertical 
deviation  of  the  lens  from  its  normal  position.  Also  this  camera  is  provided  with  a graduated 
metal  frame,  the  inner  edges  of  which  have  either  a centimetre  or  five-millimetre  graduation,  which 
is  reproduced  upon  the  margins  of  the  negatives.  They  serve  not  only  to  locate  the  horizon 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  in. 


717 


and  the  principal  lines  upon  the  perspectives,  but  they  also  give  the  means  to  discover  any  distor- 
tion that  may  arise  in  the  pictures  due  to  the  wet  process  of  development. 

This  metal  graduated  frame  is  brought  into  contact  with  the  sensitive  surface  of  the  film  by  a 
simple  mechanical  contrivance  in  such  a way  that  the  focal  length  for  all  negatives  is  constant, 
even  if  the  plate  holders  or  glass  plates  should  not  be  equally  thick. 

(G)  Col.  A.  LaussedaCs  latest  phototheodolite. — This  instrument  (ligs.  105  and  10G)  has  been 
manufactured  by  E.  Ducretet  and  L.  Lejeuue,  in  Paris,  France. 

Both  transit  telescope  L and  camera  C are  centrally 
mounted,  the  latter  above  the  former.  The  camera  may  also 
be  used  alone,  independently  of  the  transit,  and  it  may  then 
be  mounted  upon  the  tripod  (fig.  106)  by  means  of  a special 
pivot  or  spindle  S' . The  transit  may  likewise  be  used  alone, 
without  the  camera,  for  trigonometric  observations. 

/S'  - leveling  screws,  c,  = central  clamp  screw.  C — cam- 
era, and  B = magazine  for  fifteen  plates.  0 = objective  of  the 
camera;  it  is  a rectilinear  wide-angle  lens  of  75  millimetres  focal 
length.  H = sliding  front  plate  of  camera,  provided  with  pinion 
and  rack  movement,  P,  to  elevate  or  depress  the  lens.  V = 
finder  to  show  the  extent  of  the  field  covered  by  the  photo- 
graphic plate,  although  a focusing  glass,  G , fig.  106,  is  also  pro- 
vided. L = transit  telescope  provided  with  stadia  wires.  Ce  = 
vertical  circle,  graduated  to  30k  J\[  — Wye  supports  of  the  tel- 
escope axis  of  revolution,  their  prolongation  forming  the  camera 
support.  A = horizontal  circle  graduated  to  30' ; its  clamp  and 
slow-motion  screw  are  indicated  at  P'.  N = adjustable  level. 

I)  = declination  or  box  compass. 

Several  loaded  magazines,  each  containing  15  plates,  may 
be  carried  with  this  instrument  and  the  plates  may  be  exchanged 
in  full  daylight  without  having  to  remove  the  camera.  The  pho- 
tographic plates  are  61  by  9 centimetres,  but  enlarged  prints  are 

used  for  the  iconometric  platting. 

Six  plates  cover  the  entire  hori- 
zon and  will  form  a complete  pan- 
ora  m a. 

The  lens  is  provided  with  an 
iris  shutter.  It  may  be  focused  for 

short  distances  or  infinity  by  turning  a lever  over  a scale  showing  the 
distances  in  metres  attached  to  the  front  board,  H,  of  the  camera. 

In  fig.  106  the  camera  is  represented  with  the  magazine,  Z>,  removed 
and  replaced  by  the  ground  glass  plate,  G. 

The  entire  outfit,  excepting  the  tripod,  may  be  transported  in  one 
carrying  case  (with  shoulder  or  pack  straps)  of  39  by  28  by  17  centi- 
metres size  and  8 kilogrammes  weight  if  but  one  magazine  filled  with 
15  plates  is  included. 

(7)  T he  phototheodolite  of  Starke  and  Kammerer. — This  instrument, 
fig.  107,  is  somewhat  similar  in  construction  to  Professor  Finsterwal- 
der’s  phototheodolite;  both  have  neither  telescope  nor  vertical  circle, 
being  provided  with  camera  telescopes  instead. 

An  ordinary  skeleton  tripod  supports  the  three  leveling  screws,  S,  and  a central  clamp  screw 
with  spiral  spring,  P,  securely  connects  the  tripod  head  with  the  instrument  proper.  II  represents 
the  horizontal  circle,  graduated  to  20',  but  by  means  of  two  verniers  and  microscopes,  L,  horizontal 
angles  may  be  read  to  V. 

The  vertical  axis  of  revolution,  ending  in  three  horizontal  arms,  Bu  P,,  P:i,  may  be  adjusted 
with  the  aid  of  the  leveling  screws  S and  the  cross  levels  lu  lz.  The  plate  D,  forming  the  support 
of  the  cross  levels,  is  firmly  united  with  the  arm  B2. 


718 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


E = upper  clamp  screw.  M = upper  tangent  screw  for  slow  motion.  F\,  F-2,  F3  — three  level- 
ing screws  supporting  the  camera  telescope ; they  rest  in  grooves  on  the  arms  7>,,  B2,  B3.  lh  Z4  = cross 
levels,  attached  to  the  camera  telescope,  figs.  107  and  108;  they  serve  to  adjust  the  photographic 
plate  into  vertical  plane,  using  the  three  leveling  screws  Fj,  F-2,  F3  for  this  purpose.  S — movable 
front  board  or  lens  slide,  figs.  107  and  108.  Q = handle  to  facilitate  the  mounting  of  the  camera, 


C , upon  the  three  arms  B , Zt>,  B3.  /li  = pinion  for  elevating  or  depressing  the  front  board  *8, 
which  has  a corresponding  rack,  as  illustrated  in  fig.  lt>7.  K2  — differential  pinion  for  slow  motion 
of  the  front  board.  II  = clamp  screw  for  fixing  the  lens  in  any  position  above  or  below  its  central 
or  normal  position,  m = millimetre  scale  for  measuring  any  vertical  change  ot  the  lens  trom  its 
normal  position,  the  vernier  n permitting  such  change  to  be  read  to  0-05  millimetre. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


719 


The  camera  may  be  securely  united  with  the  vertical  axis  of  the  horizontal  circle  by  a clamp 
screw  manipulated  from  within  the  camera  box. 

When  the  zero  mark  of  the  vernier  n coincides  with  the  70  mark  of  the  scale  m,  the  lens  should 
be  in  its  central  or  normal  position.  The  slide  S may  be  moved  70  millimetres  up  or  down;  from 
70  to  140  it  falls  above  the  normal  position. 

The  lens  is  a Zeiss  auastigmat,  '/is,  with  a focal  length  of  about  212  millimetres. 

When  the  camera  lens  is  suitable  for  photo  topographic  purposes,  the  horizontal  change  in 
the  distance  between  its  second  nodal  point  and  the  image  plane  should  only  be: 

0-09  0T1  0-15  0-22  0- to  millimetre  for : 

distances  <>f  500  400  300  200  100  metres. 

Hence  focusing  may  be  dispensed  with  for  general  photo-topographic  purposes;  still,  in  order 
that  this  instrument — for  special  purposes — may  also  produce  sharp  and  well-defined  pictures  of 
objects  close  to  the  camera,  the  lens  mount  is  such  to  allow  a motion  in  the  direction  of  the  optical 

h, 


axis  within  a range  of  2 millimetres,  whereby  objects  but  23  metres  away  from  the  camera  may 
still  be  brought  into  focus. 

The  external  tube  of  the  lens  mount  has  a helical  groove  or  slot,  fig.  108,  in  which  a small 
metal  block  t,  provided  with  an  index  mark,  may  glide  freely.  This  block  is  attached  to  the  inner 
tube  of  the  lens  mount,  and  a screw  r at  one  end  of  the  slot  serves  to  clamp  the  two  tubes  together, 
when  the  focal  length  will  be  maintained  constant  for  any  length  of  time.  When  the  screw  r is 
loosened  and  the  outer  tube  revolved  from  left  to  right,  the  focal  length  will  be  shortened.  When 
the  block  t has  passed  from  one  end  of  the  slot  to  the  other,  the  focal  length  will  have  suffered  a 
change  of  2 millimetres.  The  two  positions  of  the  index  mark  on  the  block  t , for  these  extreme 
limits,  are  marked  on  the  edge  of  the  slot  on  the  outer  tube,  0 and  2,  fig.  108;  the  interval  being 
divided  into  twenty  equal  parts,  one  part  will  correspond  with  an  axial  motion  of  the  camera  lens 
of  0T  millimetre. 

A metal  frame  is  attached  to  the  back  of  the  camera  box,  its  rear  surface  coinciding  with  the 
picture  plane.  The  inner  edges  of  this  frame  are  provided  with  a centimetre  graduation;  the 
middle  marks  (triangular  file  cuts)  of  the  vertical  sides  of  this  frame  designate  the  termini  of 
the  horizon  line  on  the  negative,  while  the  middle  notches  of  the  two  horizontal  sides  indicate 
the  position  of  the  principal  line.  When  the  instrument  is  in  adjustment,  the  principal  line  will  be 


720 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


vertical,  the  horizon  line  will  be  horizontal,  and  their  point  of  intersection  will  be  the  principal 
point  of  the  photographic  perspective.  The  opening  of  this  metal  frame  is  17-8  by  22-8  centimetres, 
which  is  also  the  effective  size  of  the  pictures. 

The  two  frames  I and  II  in  figs.  109  and  110  give  the  means  at  hand  to  make  a light-tight 
connection  between  the  single  plate  holders  (or  ground-glass  plate)  and  the  camera  telescope.  The 
short  bellows  w,  connecting  frame  I with  II,  will  admit  the  frame  II  to  be  moved  a little  while  I 
remains  fixed  to  the  camera  box.  Each  of  these  two  frames  is  provided  with  two  hooks,  frame  J 
having  one  upper  hook  hx,  figs.  107  and  108,  and  a similar  hook  near  the  lower  corner  diagonally 
opposite  //,.  The  hook  h2,  fig.  108,  is  attached  to  the  upper  corner  (opposite  hook  7*.,)  of  frame  II, 
which  also  has  a similar  lower  hook  diagonally  opposite  li2  and  directly  under  hu 

Fig.  110  represents  a partial  section  of  the  rear  end  of  the  camera,  showing  the  ground-glass 
attachment  V.  Frame  II  is  fastened  to  frame  J by  means  of  the  upper  left 
hook  h2  and  the  lower  right  hook. 

The  ground-glass  frame  V is  supported  by  the  screws  zx  and  z2,  figs.  110 
and  111,  the  points  of  which  rest  upon  the  metal  plates  n, 
figs.  108  and  110,  attached  to  the  permanently  fixed  frame 
I.  The  face  of  the  ground  glass  O,  fig.  110,  is  brought  into 
contact  with  the  rear  surface  of  the  graduated  metal  frame 
R,  fig.  110,  by  means 
of  the  upper  right  and 
lower  left  hooks. 

The  ground-glass 
attachment  V also  has 
the  eyepiece,  which 
forms  a telescope  with 


2. 


Gl 


te: 


HJIMM 


or 


Fi  &.  109 


FiG.llO 


the  camera  lens,  converting  the  camera  into  a cam- 
era telescope.  The  position  of  the  optical  axis  of 
the  eyepiece  may  be  adjusted  vertically  by  turning 
the  screws  zx  and  z2  until  the  line  of  collimation  of 
eyepiece  and  camera  lens  fall  together  into  the  plane 
of  the  camera  horizon  (the  camera  lens  being  in  its 
normal  position,  or  the  zero  mark  of  the  vernier  n 
coinciding  with  the  70  mark  of  the  scale  m,  fig.  107). 

In  this  position  points  on  the  horizon  maybe  sighted 
through  the  eyepiece  of  the  ground-glass  attach- 
ment; but  when  the  camera  lens  had  been  moved 
up  or  down  some  distance  away  from  its  normal  position 
the  eyepiece  can  no  longer  be  used  with  its  optical  axis 
horizontal,  and  the  stops  and p2,  fig.  Ill,  are  now  unfas- 
tened and  the  eyepiece  is  tilted  up  or  down  (rotating  it 
about  the  horizontal  axis  xl  x2,  fig.  Ill)  until  its  optical 
axis  is  directed  to  the  center  of  the  object  glass,  when  the 
image  of  the  point  to  be  bisected  will  appear  well  defined. 

The  circular  oxienings  p,  shown  in  the  ground-glass  attachment,  fig.  Ill,  serve  to  examine  the 
middle  notches  of  the  inner  edges  of  the  sides  of  the  graduated  metal  frame  R,  which  define  the 
horizon,  and  the  principal  lines  of  the  perspective,  thus  giving  the  means  to  test  the  positions  of 
those  lines  and  to  adjust  the  same,  if  necessary. 

The  outer  wooden  frame  V,  fig.  110,  of  the  ground  glass  attachment  is  strengthened  with  two 
metal  diagonal  ribs  Dx,  fig.  Ill,  which  are  joined  at  their  intersection  by  a ring  r,  the  latter  form- 
ing the  support  for  the  eyepiece,  which  may  be  revolved  about  the  horizontal  axis  x\  x2,  as  has 
been  already  mentioned. 

Each  holder  contains  a single  plate,  and  fig.  109  illustrates  a section  through  the  upper  rear 
part  of  the  camera  box  with  a plate  holder  K in  position : 

R = dry  plate;  it  rests  at  its  four  corners  upon  the  springs  /.  S — hard  rubber  slide,  which 


Fi  G.  Ill 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


721 


is  completely  withdrawn  when  making  an  exposure  of  the  plate.  R = graduated  metal  frame 
permanently  fixed  to  the  rear  end  of  the  camera  box  C. 

We  will  now  describe  how  the  plate  holder  is  attached  to  the  camera  for  exposing  a plate: 

Frame  II  is  set  free  from  frame  /,  and  K is  hung  to  the  frame  II  by  means  of  the  bent  plate  l, 
fig.  109,  when  the  beveled  projecting  edge  of  K closes.into  the  rebate  of  frame  17,  producing  a light- 
tight connection.  K is  now  secured  to  frame  11  by  the  upper  left  and  lower  right  hooks  (which  is 
the  position  shown  in  fig.  109).  The  hard-rubber  slide  8 is  now  withdrawn,  and  the  pair  of  hooks — 
upper  right  and  lower  left — are  tightened  to  draw  the  holder  K 
forward  until  the  sensitive  film  surface  is  brought  into  contact  with 
the  graduated  metal  frame  R at  the  back  of  the  camera  C,  the 
springs  /taking  up  any  lost  motion  and  insuring  a perfect  contact. 

The  lens  is  now  uncapped,  the  exposure  made,  and  the  plate 
holder  is  withdrawn  by  repeating  the  same  operations  in  the  inverse 
order:  unfastening  the  pair  of  hooks — upper  right  and  lower  left — 
inserting  the  slide  8,  and  drawing  back  the  last  two  hooks — lower 
right  and  upper  left. 

(8)  Captain  HiibVs plane-table photogr ammeter. — This  instrument 
is  made  by  R.  Lechner  in  Vienna,  Austria,  and  it  has  been  described 
in  “Lechner’s  Mittheilungen  aus  dem  Gebiete  der  Photographie  und 
Ivartographie,”  Verlag  von  R.  Lechner  (Wilhelm  Muller)  Graben 
31,  Wien. 

The  result  aimed  at  in  topography  generally  being  the  graphic 
representation  of  the  terrene,  Captain  Hiibl  replaced  the  theodolite 
of  the  ordinary  pliotogrammeter  by  a plane  table  with  alidade,  thus 
being  enabled  to  plat  the  directions  required  for  the  orientation  of 
the  picture  traces,  as  well  as  those  needed  for  the  location  of  the 
camera  stations,  directly  in  the  field  upon  the  plane  table. 

For  this  purpose  the  top  M,  fig.  112,  of  the  camera  C,  (21  by 
21  centimetres)  is  disposed  for  use  as  a plane  table.  It  receives  the  paper  sheet,  which  is  held  in 
position  by  four  metal  corner  clamps  n. 

Fig.  113  shows  the  plane  table  (or  upper  surface  of  the  camera)  ab  c d,  which  has  two  pivots, 
z and  z\  about  which  the  ruler  LL  of  the  alidade  K may  be  revolved  in  azimuth.  If  z/\  fig.  113, 
represents  the  constant  focal  length,  eg  will  be  the  horizontal  projection  of  the  picture  trace.  By 

placing  the  ruler  LL  of  the  alidade  upon  the 
pivot  z the  horizontal  projections  of  horizon- 
tal directions  emanating  from  z (representing 
the  platted  station  point)  as  a center  to  those 
points  of  the  perspective  which  serve  to  ori- 
ent the  picture  may  be  drawn  upon  the  paper 
between  the  sector  e z g. 

The  central  pivot  z',  fig.  113,  serves  as 
the  vertical  axis  of  rotation  for  the  alidade 
ruler  77  when  drawing  the  horizontal  direc- 
tions to  known  points  (signals  over  trigono- 
metric stations,  visible  from  the  camera  sta- 
tion) to  locate  the  position  of  the  station 
The  line  zf  or  z'f  represents  the  horizontal 
It  is  the  trace  of  the  prin- 


Fig.  113 


with  reference  to  surrounding  triangulation  points 
projection  of  the  principal  ray  (or  of  the  optical  axis  of  the  camera), 
cipal  plane  upon  the  horizontal-projection  plane. 

With  reference  to  fig.  112: 

c = camera  box  made  ot  aluminum,  with  constant  focal  length,  k = plane-table  alidade, 
arranged  for  stadia  reading,  with  vertical  circle,  z — pivot  over  second  nodal  point  of  the  camera 
lens.  z]  = pivot  vertically  above  center  of  instrument  (in  prolongation  of  the  vertical  axis  of 
rotation  for  the  camera  or  plane-table). 

GTS  1 1(1 


722 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


At  e and  g,  fig.  113,  are  two  stops  representing  the  ends  of  the  photographic  field  ezg , which 
is  identical  with  the  horizontal  angle  commanded  by  each  plate. 

The  lever  h,  fig.  112,  serves  to  locate  the  principal  point  /,  fig.  113;  when  the  edge  of  the  ruler 
LL  abuts  against  the  upturned  lever  li,  and  the  principal  ray  zf  (bisecting  the  angle  ezg)  may  be 
drawn  upon  the  plane-table  sheet. 

With  reference  to  fig.  112 : b = rubber  bulb  for  operating  the  pneumatic  shutter  of  the  camera. 
t = head  of  pinion  which  serves  to  elevate  or  depress  the  camera  lens,  the  change  from  the  normal 
position  of  the  lens  being  read  on  a scale  with  vernier,  n = spirit  level,  two  being  provided  (at 
right  angles)  for  adjusting  the  instrument.  R = movable  plate  carrier.  LL  = lever  for  moving 
the  plate  carrier  R forward  (toward  the  lens)  until  the  sensitive  surface  of  the  plate  is  brought 
into  contact  with  the  graduated  metal  frame  vv. 

The  horizon  and  the  principal  line  may  be  located  upon  the  perspectives  by  means  of  the 
centimetre  graduations  on  the  inner  edges  of  the  metal  frame  vv,  or  two  fine  wires  may  be  attached 
to  the  corresponding  points  of  the  graduation. 

The  camera  is  supported  by  the  three  leading  screws  s,  their  upper  ends  resting  in  three  slots 
of  the  lower  face  of  the  camera  box.  The  latter  is  firmly  united  with  the  tripod  head  by  means  of 
a central  clamp  screw  with  spiral  spring.  T=graduated  horizontal  circle  with  clamp  screw.  It 
serves  to  enable  the  observer  to  turn  the  camera  by  an  equal  amount  in  azimuth  after  each  expos- 
ure. xx= correction  screws  to  adjust  the  graduated  metal  frame  vv  to  bring  the  principal  point 
into  the  optical  axis  of  the  camera  lens. 

The  plane-table  M,  with  alidade  K,  serves  to  locate  the  camera  station  in  both  the  vertical 
and  horizontal  sense.  If  the  camera  stations  are  not  very  close  together,  the  plane-table  may  also 
serve  for  the  location  of  tertiary  points  and  for  the  sketching  of  details. 

This  photographic  plane-table  is  well  suited  for  topographic  reconnaissance  surveys.  The 
results  obtained  by  means  of  the  same  may  not  be  as  precise  as  those  obtained  with  the  more 
complicated  and  refined  phototheodolites,  but  it  is  more  easily  transported,  is  very  simple  in 
manipulation,  and  the  adjustments  are  not  liable  to  be  easily  disturbed.  The  instrument  is 
compact,  well  conceived,  and  excellently  executed. 

The  size  of  the  photographic  plate  is  12  by  16  centimetres,  giving  an  effective  picture  within 
the  graduated  margin  of  10  by  14  centimetres. 

The  cube  shaped  camera  has  sides  of  21  centimetres  length,  and  weighs  3-5  kilograms.  The 
packing  case,  including  the  entire  outfit  and  stout  tripod  (three  folding  legs),  weighs  only  1T5 
kilograms.  The  cost  in  Vienna  of  the  complete  instrument  is  400  florins. 

V.  PANORAMIC  CAMERAS. 

The  lenses  of  the  older  surveying  cameras  gave  correct  perspectives  only  for  small  angles, 
rarely  exceeding  30°,  and  Martens,  in  Paris,  was  probably  the  first  to  devise  a so-called  panoramic 
camera  to  photograph  larger  sections  of  the  horizon  on  one  plate,  even  with  lenses  that  ordinarily 
would  cover  but  a small  angular  field. 

If  the  objects  to  be  photographed  are  far  enough  distant  to  permit  the  use  of  a constant  focal 
length  of  lens  for  the  picture,  and  if  the  lens  may  be  rotated  about  a vertical  axis  passing  through 
the  second  nodal  point  of  the  lens  system,  such  panoramic  views  may  be  obtained  upon  a sensitized 
surface  bent  into  a half  cylinder  whose  radius  equals  the  constant  focal  length  of  the  lens  and 
whose  axis  coincides  with  the  vertical  axis  of  rotation  of  the  camera  lens. 

The  topographic  cylindrograpli  of  R.  Moessard. — The  following-described  apparatus  has  been 
devised  by  R.  Moessard  (commandant  du  Genie,  attache  au  service  geographique  de  l’armf‘e),  of 
St.  Cyr,  France. 

The  liemicylindrical  camera  box,  fig.  114,  rests  upon  a tripod,  with  three  leveling  screws  to 
adjust  the  vertieality  of  the  axis  of  revolution  aa  of  the  camera  lens  0,  which  axis  coincides  with 
that  of  the  half  cylinder  formed  by  the  sensitized  surface  of  the  film.  The  latter  may  be  replaced 
by  a half-cylindrical  ground-glass  plate. 

The  camera  lens  0 may  be  rotated  by  hand  about  aa,  using  the  sight  ruler  8 as  lever.  By 
viewing  the  landscape  through  the  sights  PR'  of^the  lever  8,  the  proper  timing  for  the  exposure 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


723 


of  the  different  panorama  sections  may  be  estimated.  The  space 
between  the  lens  0 and  the  frame  RR  is  filled  in  with  a light-tight 
fabric,  allowing  full  play  for  the  rotating  objective  0. 

The  upper  surface  of  the  topo- 
graphic cylindrograph  is  provided  with 
an  azimuth  compass  C and  a pair  of 
cross  levels  A and  B.  The  bent  frame 
forming  the  guide  for  the  sensitive  film 
has  graduations  on  the  inner  edges, 
which  form  the  margins  of  each  pano- 
ramic view. 

The  divisions  of  the  upper  and 
lower  (horizontal)  scales  correspond  to 
degrees  in  arc,  while  the  divisions  of 
the  vertical  sides  are  graduated  to  read 

1*^,  where  /=  constant  focal  length  of 

the  lens  0 = radius  of  the  cylindrical 
sensitive  surface  of  the  film. 

Four  movable  indices  are  provided, 
two,  H and  H1,  fig.  115,  serve  to  mark 
the  horizon  line  of  the  half  panorama, 
and  the  other  two,  E and  E,  indicate  the 
magnetic  north  and-south  line  and  the 
magnetic  east-and-west  line  for  each 
half  panorama,  the  compass  0,  with  the 
sight  ruler  IS,  giving  the  means  for  prop- 
el ly  setting  the  index  marks  N and  E 
for  each  view.  Thus  the  magnetic  azi- 
muths of  horizontal  directions  may  be 
taken  directly  from  the  pictures. 

The  vertical  angles  are  readily 


H 

► 

r~ 

N 

a' 

lk 

~r~ 

E. 

H' 

I 

V 

^ 

T A 

found  by  means  of  the  ordi- 
nates of  pictured  points 
(above  or  below  the  horizon 
line  HE')  measured  in  one- 
hundredths  of  the  focal 
length  /,  using  the  photo- 
graphed scales  on  tlie  verti- 
cal margins  of  the  pictures 
for  this  purpose. 

For  example:  The  an- 
gle of  depression  of  the  ray 
Oa  (to  the  base  of  the  pic- 
tured tree 

«),  fig- 

maybe  found 
from 


tan  /j  — 


act/ 


Fig. 1 15 


724 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


or  when  aa',  measured  on  the  side  scale,  is  found  to  be  equal  to  25  divisional  parts: 

tan  7?  = ^ = 0.25 


\ 


/ 


To  determine  whether  the  levels  A and  B,  fig.  114,  read  zero  when  the  cylindrical  film  is  ver- 
tical, and  also  to  ascertain  whether  the  index  marks  H and  H ',  fig.  115,  representing  the  horizon 
line,  are  correctly  placed,  we  may  proceed'  as  follows: 

A theodolite,  fig.  116,  is  set  up  about  10  or  15  metres  behind  the  cylindrograph  (after  the 
back  of  the  camera  had  been  removed  to  bring  the  index  marks  H and  H'  into  view),  and  both 
instruments  are  leveled.  After  bisecting  the  upper  edge  of  the  cyliudrograph  the  telescope  of  the 
theodolite  is  moved  in  azimuth,  when  the  bisection  should  continue.  The  same  should  be  the  case 
lor  the  lower  surface  edge  of  the  cylindrograph  after  depressing  the  telescope  of  the  theodolite  to 

bisect  that  edge.  Does  this  not  take  place,  the  cylindrograph  will 
have  to  be  adjusted  by  means  of  the  leveling  screws  until  the  bisec- 
tion takes  place,  when  the  level  A is  to  be  changed  to  read  zero  for 
this  position  of  the  cylindrograph. 

The  theodolite  is  now  set  up  in  the  direction  of  the  level  A,  at 
one  side  of  the  cylindrograph,  and  the  level  B is  adjusted  in  the 
same  manner  as  just  indicated  for  A. 

To  adjust  the  indices  H and  H'  into  the  horizontal  plane  (con- 
taining the  optical  axis  of  the  adjusted  cylindrograph)  a comparison 
may  be  made  on  a cylindrograph  picture,  showing  several  points  of 
known  elevations,  the  elevation  of  the  cylindrograph  being  also 
known,  or  the  theodolite  may  be  set  up  with  the  horizontal  telescope 
at  the  same  elevation  with  the  optical  axis  of  the  adjusted  cylindro- 
graph. The  horizontal  telescope  of  the  theodolite  is  now  moved  in 
azimuth  until  a well-defined  point  is  bisected,  which  point  may  be 
identified  on  the  ground  glass  of  the  cylindrograph.  The  image  of 
this  point  on  the  ground  glass  is  marked  and  the  cylindrograph  is 
moved  in  azimuth,  marking  the  image  on  the  ground  glass  in  two 
more  places.  A (horizontal)  line  passing  through  these  marked 
points  should  pass  through  H and  H' . 

The  objective  0 is  attached  to  a funnel-shaped  box  within  the 
camera,  permitting  tire  simultaneous  exposure  of  a vertical  strip  of 
film  having  a width  of  but  62  millimetres.  Points  of  the  film  that 
would  be  pictured  outside  of  this  strip  can  not  be  acted  upon  by 
the  light  unless  the  objective  is  revolved  about  the  axis  aa. 

After  the  time  needed  for  the  correct  exposure  of  this  strip  (of 
62  millimetres  width)  has  been  ascertained,  the  correct  exposure 
may  be  given  the  entire  semicylinder  by  moving  the  sight  ruler  S 
with  a quick  and  uniform  motion  about  aa  from  one  extreme  end  of  the  film  to  the  other. 

The  semicylindrical  film  being  860  millimetres  long,  each  strip  of  the  film  would  then  have  been 
exposed  the  sixty-two  eight  hundred  and  sixtieth  part  of  the  time  required  to  make  one  full  revo- 
lution of  the  objective.  If  one  complete  revolution  required  teu  seconds,  and  if  the  correct  expo- 
sure for  the  strip  was  found  to  be  five  seconds,  each  strip  would  have  received  an  exposure  of 

1 0 x seconds  = 0.72  second.  To  give  each  strip  the  required  exposure  of  five  seconds  the  entire 
860 

revolution  of  the  lens  should  be  repeated  0~T>  times  in  succession,  or  about  seven  times,  each  com- 
plete revolution  taking  ten  seconds. 

As  yet  these  instruments  are  not  made  sufficiently  precise  to  be  recommended  for  phototopo- 
graph ic  surveys.  The  conception  of  this  instrument,  however,  is  ingenious,  and  where  the  ques- 
tion of  transportation  need  not  be  considered  the  topographic  cylindrograph  in  a more  perfected 
form  may  give  good  results  for  surveying  purposes. 


/ 


/ FiG.  "6 


/ 


\ 


'6  THEODOLITE. 


CHAPTER  Y. 


ICONOMETERS  AND  PERSPECTOGRAPHS. 


We  understand  under  iconoineters  a series  of  instruments  that  have  been  devised  to  simplify 
the  constructions  of  pliototopograpliic  platting  (iconometry). 

After  two  drawing  boards  have  been  covered  with  paper  (gummed  down  on  the  edges)  both 
sheets  are  provided  with  a chart  projection  upon  which  all  trigonometric  (triangulation)  points 
are  platted  and  their  elevations  inscribed. 

The  constructions  incidental  to  the  iconometric  platting  of  the  phototopographic  survey  may 
be  divided  into  three  classes: 

First.  The  platting  of  all  horizontal  directions,  that  had  been  observed  instrumentally,  for  the 

location  of  the  camera  stations  and  for  the  orientation 
of  the  panorama  views. 

Second.  The  determination  of  the  horizontal  pro- 
jection of  points  pictured  on  three  or  more  photographs 
taken  from  different  stations. 

Third.  The  determination  of  the  elevations  of  the 
various  camera  stations  and  tertiary  pdints  (that  are 
located  iconometrically)  to  facilitate  the  platting  of 
the  horizontal  contours  of  the  terrene. 

The  principal  instruments  used  for  the  iconometric 

platting  of  the  phototop- 
ographic survey  in  Italy 
have  been  described  in 
Appendix  No.  3 of  the 
United  States  Coast  and 
Geodetic  Survey  Report 
for  1893.  They  are: 

I.  The  graphic  pro- 
tractor. — It  is  used  for 
platting  horizontal  direc- 
tions observed  instrumen 

II.  The  graphic  sector 


© o © I 

L 

\ 

Fig. 1 17 


nini,  serves  to  plat  hori 
without  first  drawing  the 

III.  The  graphic  hyp 
Paganini.  It  serves  to 
as  well  as  points  platted 
the  intersections  of  lines 
IY.  The  centrolinead. 


tally  in  the  field  on  the  platting  sheet  in  the  office, 
“settore  grafico”). — This  instrument,  devised  by  Paga- 
zontal  directions  to  points  pictured  on  the  photographs 
picture  traces  on  the  working  sheet. 
someter.  — This  instrument  has  also  been  invented  by 
determine  the  elevations  of  all  points  (camera  stations, 
from  the  photographs)  platted  on  the  working  sheet  by 
of  direction. 

Reference  has  been  made  to  this  instrument  under  the  description  of 
the  Canadian  photograph  board.  Captain  Deville  uses  this  instrument  for  drawing  lines  to  a 
vanishing  point  falling  outside  of  the  limits  of  the  platting  sheet. 

The  distance  between  the  principal  point  and  the  vanishing  points  of  lines  increases  the  nearer 
parallel  to  the  picture  plane  such  lines  are.  Lines  parallel  with  the  picture  plane  have  their  van- 
ishing point  at  infinite  distance  from  the  principal  point;  practically  they  have  no  vanishing 
point.  Their  perspectives  are  parallel  with  the  original  lines. 

It  often  occurs  in  iconometric  platting  that  the  vanishing  points  of  some  lines  fall  outside  of 
the  limits  of  the  drawing  board,  and,  in  order  to  draw  a line  which,  if  produced,  would  pass  through 
the  distant  vanishing  point,  special  constructions  would  have  to  be  made  to  locate  the  direction 
of  such  a line. 

This  instrument,  fig.  117,  is  used  instead  of  making  such  auxiliary  constructions  on  the 
photograph  board.  It  is  composed  of  a wooden  straightedge,  L,  and  two  wooden  movable  arms, 


726 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


I and  l',  which  may  be  given  any  inclination  against  the  straightedge  L.  The  clamp  screws,  r and 
r',  serve  to  fix  the  arms  l and  l'  permanently  in  any  position. 

The  photograph  board,  fig.  70,  is  provided  with  four  points,  A,  B,  C,  and  E,  indicating  the 
centers  of  the  studs  against  which  the  arms  l and  l'  play  or  rest  when  the  centrolinead  is  used  on 
the  photograph  board.  The  distance  between  the  studs  may  vary,  but  each  two  forming  a pair 
are  generally  placed  from  G to  8 inches  apart,  and,  the  arms  of  the  centrolinead  being  held  in 
contact  with  the  studs,  the  various  directions  of  the  ruler  L will  intersect  each  other  in  one 
common  point. 

With  reference  to  fig.  118  we  have: 

A and  B = one  pair  of  studs  permanently  fixed  upon  the  photograph  board.  OA  and  OB  = 
movable  arms  of  the  centrolinead,  now  clamped  in  the  position  given  them  in  the  figure.  OG  = 
ruler  of  the  centrolinead  (=  L in  fig.  117). 

If  we  describe  a circle  through  the  three  points  A,  0,  and  B— the  angle  AOB  remaining 
constant— the  angle  AOB  will  be  an  angle  of  the  periphery  AB  for  any  position  given  the  ruler 
OG  (=  L,  fig.  117)  as  long  as  OA  and  OB  ( l and  V,  fig.  117)  remain  in  contact  with  the  studs  A 
and  B.  When  OG  is  changed  to  assume  the  position  O’C  the  intersection,  V,  of  the  two  lines 
OC  and  O'C'  will  also  be  on  the  periphery  of  the  circle  because  the  angle  AOV(AO'V)  remains 
the  same  and  must  subtend  the  same  arc  A Fas  long  as  the  studs  A and  B remain  unchanged. 

Hence,  for  the  assumed  position  of 
the  studs  the  directions  of  all  lines 
drawn  along  the  fiducial  edge  of  the 
ruler  OG  (giving  0 all  positions  on 
the  arc  AOB)  will  pass  through  the 
point  V- — they  will  vanish  at  V. 

In  the  icouometric  work  of  the 
Canadian  surveys  the  centrolinead  is 
used  only  for  drawing  the  perspec- 
tives of  horizontal  lines,  their  vanish- 
ing points  being  on  the  horizon  line. 
The  studs  A and  B are  placed  on  the 
photograph  board  on  a line  AB,  per- 
pendicular to  the  horizon  line  and  at 
equal  distances  from  the  latter.  The 
horizon  line  RIB  (Bf)1  in  fig.  70) 
becomes  a diameter  of  the  circle  AOBV,  and  VA  — VB.  If  the  movable  arms  of  the  centrolinead 
include  the  same  angles  with  the  direction  of  the  fiducial  edge  of  the  straightedge,  the  line  OC, 
bisecting  the  angle  AOB,  must  pass  through  U midway  between  A and  B. 

The  distance  of  the  vanishing  point,  V,  from  the  principal  point,  P,  may  be  varied  at  pleasure 
by  changing  the  inclination  of  the  arms,  / and  l',  against  the  direction  of  the  fiducial  edge  of  the 
ruler  L.  When  the  direction  of  the  arms  l and  V falls  together  and  is  perpendicular  to  L,  the 
vanishing  point  will  fall  at  infinite  distance  from  the  principal  point  P and  the  lines  drawn  along 
the  fiducial  edge  of  the  straightedge  L will  become  parallel  with  the  horizon  line  HR'. 

The  distance  of  the  vanishing  point  V from  P may  also  be  varied  by  changing  the  distance 
between  the  studs  A and  B or  G and  E,  fig  70 — increasing  this  distance  will  enlarge  the  circle 
AOB  V and  V moves  farther  off  from  P,  reducing  that  distance  will  decrease  the  diameter  of  the 
circle  AOBV  and  V will  approach  the  principal  point  P.  The  practice  in  Canada,  however,  is  to 
retain  the  position  of  the  studs  unchanged  on  the  photograph  board  and  to  change  the  inclination 
of  the  arms  l and  V of  the  centrolinead  instead. 

If  we  gradually  close  the  arms  l and  l',  V will  approach  the  line  AB  and  when  the  angle  AOB 
becomes  equal  to  90°  the  arc  AOB  will  have  become  a semicircle,  and  the  intersection  of  AB  with 
RIB  will  be  the  center  of  the  circle 
B 


iOBV,  the  distance  of  both  0 and  Ffroin  AB  will  be  equal 


to 


continuing  to  close  the  arms  l and  V,  V will  approach  closer  to  AB  without  ever 


reaching  it 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


727 


( l ) To  set  the  arms  (l  and  l')  of  the  centrolinead  if  the  direction  to  the  vanishing  point  ( V)  is  given 
by  a line  in  the  ground  plan. 

With  reference  to  fig.  119  we  have: 

P = principal  point  on  the  photograph  board.  A and  B = positions  of  the  studs.  Sv  = given 
direction  of  the  line  on  the  ground  plan,  when  V will  be  the  vanishing  point  for  that  line. 

We  revolve  the  picture  plane  about  the  horizon  line,  as  axis,  into  the  horizontal  platting  plane 
when  the  station  may  fall  in  S,  fig.  119,  SP  being  then  the  distance  line  or  focal  length  projected 
into  horizontal  plan.  Should  the  point  V fall  upon  the  drawing  board  we  could  describe  a circle 
through  AB  and  V and 
place  the  fiducial  edge  of 
the  centrolinead’s  straight- 
edge upon  DP  (upon  the 
horizon  line)  with  the  axis 
of  rotation  0 of  the  arms 
l and  V in  D upon  the  cir- 
cle, then  bring  the  arms  l 
and  V into  contact  with 
the  studs  A and  B and 
clamp  them  in  this  posi- 
tion. Still,  in  this  ease 
there  would  be  no  use  for 
tlie  centrolinead,  the  point 
V being  accessible. 

To  set  the  arms  for 

an  inaccessible  point  V we  again  refer  to  fig.  119.  Join  the  points  V and  B,  the  angle  VDB — the 
inclination  of  the  lower  arm  l'  against  the  ruler  L — is  equal  to  VBA,  both  angles  subtending  equal 
arcs  of  the  same  circle.  Ilraw  the  lines  CS  and  BS.  At  any  point  c on  CS  draw  cM  and  cv  par- 
allel to  AB  and  DP  and  join  b and  v.  By  reason  of  similarity  of  triangles,  vb  must  be  parallel  to 
VB  and  the  angle 

vbc  = VBC  - BDV. 


Hence,  the  arms  of  the  centrolinead  may  be  set  in  the  case  under  consideration  by  placing  the  ruler 
L on  Mb,  the  axis  of  rotation,  0,  coinciding  with  b,  and  adjusting  the  lower  arm  l'  of  the  centro- 
linead to  coincide  with  bv.  The  other  arm  I,  having  the  same  inclination  against  the  ruler  L as 
the  arm  V,  may  be  set  by  placing  the  ruler  L upon  the  horizon  line  DP  and  moving  it  along  this 

line  until  the  lower  adjusted  arm  l'  comes 
into  contact  with  the  stud  B,  then  moving 
the  other  arm  l about  0 until  it  comes  into 
contact  with  the  stud  A and  clamping  it  also. 

The  lines  BS,  CS,  Me,  and  cv  are  drawn 
once  for  all  upon  the  photograph  board,  fig. 
70.  The  only  line  to  be  drawn  for  setting  the 
arms  of  the  centrolinead  is  Sv,  which  is  the 
direction  of  the  given  line  on  the  ground 
plan.  The  line  bv  need  not  be  drawn,  the 
points  b and  v being  located  by  drawing  cv 
parallel  with,  tne  nonzon  line  and  a\l  or  cb  parallel  with  the  distance  line  SP. 

{2)  To  set  the  arms  of  the  centrolinead , if  the  given  line  VB  belongs  to  the  perspective: 

Take  any  point  F , fig.  120,  on  the  horizon  line,  join  F with  E and  F with  B,  then  draw  cM 
parallel  to  AB.  Through  e draw  ev  parallel  to  EV  and  join  vb.  Owing  to  the  similarity  of  tri- 
angles vb  will  be  parallel  with  VB  and  the  angle  vbc  = VBA,  which  is  the  inclination  of  the  arm 
against  the  ruler  L of  the  centrolinead. 

FB  and  cM  are  permanently  drawn  on  the  photograph  board,  but  FE  and  ve  will  have  to  be 
drawn  for  every  given  line.  In  this  case  two  lines  will  have  to  be  drawn  instead  of  one,  as  in  the 
preceding  case. 


A 


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UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


Centrolineads  are  usually  sold  in  pairs;  one  serves  to  work  on  the  left  side  of  the  principal 
point  and  the  other  on  the  right  side. 

V.  The perspectometer  (as  used  by  Capt.  E.  Deville). — The  perspectometer  is  used  to  dispense 
with  the  construction  of  the  squares  on  the  perspective  when  applying  the  11  method  of  squares” 
(Chapter  I,  Paragraph  IX)  to  draw  a figure  in  the  ground  plan  by  means  of  its  perspective. 

On  a thin,  transparent  film  (glass,  xylonite,  isinglass,  born,  etc.,)  two  parallel  lines  AB  and 
DIJ',  fig.  121,  are  drawn  intersecting  the  common  perpendicular  pP.  Make  DP—PD'=pA=pB= 
distance  line  (focal  length)  and  fronip  lay  off  on  AB  (to  both  sides  oip)  equal  distances: 


pm  = mn  = no  .......  =pm'=m'n'—n'o'= 

Join  these  points  of  division  to  P and  draw  lines  through  the  corresponding  intersections  of  the 

radials  from  P with  the-  perpendiculars  AD  and  BD1,  rr\  W which  lines  will 

be  parallel  with  AB  and  DD1. 

The  use  of  the  perspectometer.  —The  perspectometer  is  placed  upon  a perspective  with  P on 
the  principal  point  and  DD'  coinciding  with  the  horizon  line.  The  ground  line  of  the  perspective 
may  fall  in  XI7,  fig.  121,  it  will  be  divided  into  equal  parts  by  the  radials  from  P,  and  the  trape- 
zoids of  the  perspectometer 

d P o'  represent  the  perspectives  of 

the  squares  in  the  ground 
plane  having  the  equal  parts 
on  XX  as  sides. 

By  placing  the  perspecto- 
meter on  the  perspective  in 
the  manner  indicated  above 
the  squares  covering  the  per- 
spective of  the  figure  that  is 
to  be  platted  iconometrically 
on  the  ground  plan  are  at  once 
apparent,  and  only  those  re- 
quired for  the  drawing  of  the 
figure  in  question  are  drawn 
on  the  ground  plan. 

The  sides  of  the  squares  to  be  drawn  on  the  ground  plan  (their  side  lengths  are  equal  to  the 
divisions  on  the  ground  line  between  the  radials  drawn  from  P)  are  laid  off  from  the  trace  of  the 
principal  plane  on  the  ground  line,  and  the  position  of  the  front  line  nearest  the  picture  trace 
(or  ground  line)  is  laid  off  on  the  ground  plan  either  by  estimation  or  construction.  The  estima- 
tion of  the  position  of  this  line  (corresponding  to  tV)  on  the  ground  plan  is  made  by  noting  the 
fraction  of  a square’s  side  which  represents  the  distance  (between  W and  XX,  fig.  121)  from  the 
ground  line  on  the  perspective. 

The  same  perspectometer  serves  only  for  perspectives  which  have  the  same  distance  line 
(like  photographs  of  distant  objects  taken  with  the  same  lens),  different  distance  lines  requiring 
differ  e:  i t perspectometer s. 

The  width  p P should  be  equal  to  the  height  of  the  horizon  line  above  the  foot  of  the  picture; 
the  radials  from  P need  not  extend  beyond  the  width  of  the  picture,  the  distance  points  I)  and  IT 
having  been  taken  as  the  limit  of  the  perspectometer  in  the  figure  (121)  merely  to  show  more 
fully  the  principles  involved  in  its  construction. 

The  length  of  a single  division  on  the  line  AB  should  be  selected  with  reference  to  the  resulting 
equal  division  lengthsof  the  lowest  ground  line  usedfor  the  pictures,  as  the  dimensions  of  thedivision 
lengths  on  the  latter  give  the  measure  for  the  sides  of  the  squares  to  be  drawn  on  the  ground  plan. 

These  division  lengths  on  the  ground  line  should  be  in  harmony  with  the  scale  of  the  plan  and 
with  the  degree  of  accuracy  that  may  be  required  for  the  delineation  of  the  topographic  features. 
The  smaller  the  size  of  the  squares  is  selected  on  the  ground  plan  the  more  accurately  the  trans- 
fer of  the  figure  from  its  perspective  to  the  ground  plan  may  be  made,  the  same  principles  being 
involved  in  this  method  of  icouometric  platting  as  in  the  well-known  method  of  reducing  drawings 
by  means  of  two  sets  of  (hair)  squares,  the  ratio  of  their  sides  corresponding  to  the  scale  of  the 
required  reduction. 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


729 


Captain  Deville  recommends  the  perspectoineter  to  be  made  by  first  drawing  it  on  paper  in  a 
fairly  large  scale,  and  then  making  a negative  of  it,  reduced  photographically  to  the  desired  size 
of  the  finished  perspectoineter.  A positive  copy  may  now  be  made  on  a transparency  plate,  which, 
if  bleached  in  a solution  of  bichloride  of  mercury,  will  show  white  lines  on  clear  glass.  For  the 
sake  of  better  preservation  such  perspectoineter,  when  completely  dry  and  hard,  should  be  var- 
nished. 

When  using  the  perspectoineter  for  transferring  figures  from  their  perspectives  to  the  ground 
plan,  Avhen  such  figures  are  situated  in  planes  perpendicular  to  the  picture  plane  but  inclined 
against  the  horizon  plane,  the  center  of  the  perspectoineter  is  placed  upon  the  principal  point  P 
of  the  picture  plane,  the  same  as  before,  but  the  perspectoineter  is  now  revolved  about  P until  the 
parallel  lines  of  the  same  are  parallel  with  the  trace  of  the  inclined  (figure’s)  plane  on  the  picture 
plane.  In  this  case  the  trapezoids  of  the  perspectoineter  represent  the  perspective  of  a net  of 
squares  situated  in  the  inclined  plane,  the  squares  of  which  are  now  to  be  projected  into  the 
ground  plane. 

This  net  of  squares  in  the  inclined  plane,  when  projected  into  the  ground  plane,  will  be  com- 
posed of  rectangular  figures  of  equal  size,  their  long  sides  being  in  a direction  at  right  angles  to 
the  picture  trace  (or  ground  line)  and  of  a length  equal  to  that  which  is  intercepted  between  two 
adjoining  radials  of  the  perspectoineter  on  the  trace  of  the  inclined  plane  (on  the  picture  plane), 
while  the  short  sides  of  those  rectangles  (forming  the  projection  in  the  ground  plan  of  the  squares 
in  the  inclined  figure’s  plane)  will  be  equal  to  the  lengths  obtained  on  the  ground  line  by  project- 
ing the  points  of  intersection  of  the  radials  of  the  perspectoineter  with  the  inclined  plane’s  trace 
on  the  picture  plane  upon  the  ground  line  of  the  picture  plane. 

The  construction  of  the  rectangular  net  on  the  ground  plan  may  now  be  made  in  an  analogous 
manner  to  that  mentioned  for  the  squares,  and  the  drawing  in  of  the  figure  on  the  ground  plan 
with  reference  to  its  position  within  the  trapezoids  of  the  perspectoineter  is  accomplished  in  the 
usual  manner. 

Should  the  figures  be  situated  in  planes  that  are  inclined  to  both  the  picture  and  the  ground 
planes,  then  the  figure  is  first  projected  upon  a plane  perpendicular  to  the  picture  plane,  and 
having  the  same  trace  in  the  latter  as  the  inclined  plane. 

IT.  The  perspectograph. — Numerous  instruments  have  been  devised  for  drawing  perspectives 
from  plans  or  from  nature,  mechanically,  or  by  means  of  optical  devices,  some  of  which  may 
inversely  become  of  use  for  transcribing  perspectives  of  figures  into  orthogonal  projections. 

The  perspectograph,  invented  by  H.  Fitter,  serves  to  construct  the  orthogonal  projection  of  a 
plane  figure  from  its  perspective,  or  to  draw  the  perspective  from  the  plans  of  the  object  without 
referring  to  the  object  itself. 

Fitter’s  instrument,  manufactured  by  C.  Schroeder  & Co.,  in  Frankfort-on-the-Main,  lias  been 
patented  in  Germany,  October  13,  1883,  under  No.  29002.  It  was  devised  primarily  for  archi- 
tectural purposes. 

This  instrument  in  its  present  form,  composed  largely  of  wood,  is  not  well  suited  for  surveying- 
purposes,  as  it  contains  too  many  sources  of  error  due  to  lost  motion  in  its  bearings,  still,  its  theory 
being  sound,  there  is  no  reason  to  question  its  ultimate  value,  even  for  precise  work,  if  it  were 
caretully  made  by  an  expert  mechanician  (excluding  the  use  of  wood  and  using  metal  throughout), 
being  guided  in  its  construction  by  the  demands  of  the  greatest  precision  attainable.  As  a care- 
fully constructed  instrument  based  on  the  present  pattern  may  become  useful  in  platting  the  data 
ot  a topographic  reconnaissance  where,  in  the  nature  of  the  work,  rapidity  in  making  the  results 
practically  available  is  of  greater  importance  than  a high  degree  of  accuracy,  the  following- 
description  of  this  instrument  may  not  be  out  of  place  here.  For  its  methods  of  use  in  photo- 
topographic  surveying  we  respectfully  refer  to  Oapt.  E.  Deville’s  work  on  “Photographic 
Surveying”  already  mentioned. 

AVe  have  seen  (Chapter  I)  that  the  platted  position  of  a point  in  tlie  ground  plan  may  be 
found  from  its  perspective  (in  vertical  plane)  by  locating  the  point  of  intersection  of  the  horizontal 
projection  of  the  ray:  “station — pictured  point”  with  the  line  of  direction  itself.  (The  latter  with 
its  vertical  plane  is  revolved  about  the  trace  of  the  vertical  plane  in  the  ground  plane  (as  axis  of 
rotation)  into  the  ground  plane  in  which  plane  the  point  of  intersection  is  located.) 


730 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


With  reference  to  fig.  122  we  have: 

8 = camera  station  or  point  of  view.  /<  = perspective  (image)  of  a point  ill,  to  be  platted  in 
the  ground  plan,  s = foot  of  the  station  8.  XT  — ground  line  of  the  picture  plane  (vertical)  MX. 
M = platted  position  of  the  point  M in  the  ground  plane  GG. 

If  we  draw  through  the  foot  of  the  station  s a line  parallel  to  the  ground  line  XT,  and  make 
its  length  s (8),  equal  to  sS,  join 
(8)  and  the  platted  point  M,  then 
it  will  follow  from  the  similarity 
of  the  triangles  OfiM  and  sSM 
that: 

sS  : Ofi  = Ms  : MO 

From  the  similar  triangles 
s(S)M  and  0(/a)M  we  find 

s(8)  : O(pt)  = Ms  : MO 
hence 

s(S)  : 0(/j)  = sS  : Of  a 

Having  made  sS  = s(8 ),  the 
last  equation  can  only  prevail  if 

Ofl  — OiyfA). 

To  find,  therefore,  the  per- 
spective ft  of  a point  M,  given  on 
the  ground  plan,  we  first  draw  a 
line  s {8)  through  the  platted  sta- 
tion in  the  ground  plane  parallel 
with  the  ground  line  XY,  mak- 
ing s(S)  — height  of  the  station  8 
above  the  ground  plane.  I daw 
the  lines  sM  and  (8)M,  which  will 
intersect  the  ground  line  XY,  in 
O and  (/a),  fig.  123.  On  the  .ground  line  X‘Y',  drawn  in  another  place  of  the  working  sheet,  we 
assume  a point  O',  representing  O of  the  ground  plan,  and  erect  Ofx  perpendicular  to  X'  I ' in  O' 

and  make  O' fi  = O(fj),  when  /<  will  be  the  per- 
spective of  M in  the  reverse  position  of  the 
perspective.  The  perspective  of  any  other 
point,  IN,  given  on  the  ground  plan  may  be 
found  in  the  same  way,  making  O'Q'  = OQ 
and  Q'v  = Q{v). 

Ritter  devised  the  perspectograph  to  per- 
form this  construction,  illustrated  in  fig.  123, 
mechanically. 

Fig.  124  illustrates  the  general  arrange- 
ment of  Ritter’s  perspectograph.  sM  and 
(8)M  = two  slotted  wooden  arms  carrying 
the  tracer,  M,  at  their  point  of  intersection. 

The  connections  at  s,  0,  (8),  and  (//)  are 
such  that  the  rulers  sM  and  (S)M  may  slide 
through  these  points.  The  slide  connections, 
s and  (8),  may  also  be  moved  along  the 
groove  or  slot  of  the  wooden  ruler  RT.  The 
sliding  piece  0 is  secured  to  a rod  which  in 
turn  may  slide  in  the  groove  of  the  wooden  ruler  XY,  being  connected  at  its  other  end  I)  with  a 
system  of  arms  or  levers  joined  together  after  the  manner  of  a pantograph.  The  distance  01) 
is  maintained  unchanged  while  the  instrument  is  in  use. 


(Si 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


731 


The  center  of  s is  placed  directly  upon  the  point  that  marks  the  platted  camera  station  on 
the  ground  plan.  The  ruler  RTis  placed  parallel  to  the  ground  line  of  the  picture  plane,  and  s and 
RT  are  now  secured  in  this  position  on  the  ground  plan. 

When  the  arm  sM  is  moved,  s being  held  in  a fixed  position  (to  coincide  with  the. platted 
station  point),  the  point  0 will  follow  the  motions  of  the  arm  sM,  also  applying  its  motion  directly  to 
the  arm  OD  (which  slides  in  the  groove  of  XY)  and  indirectly  to  the  arms  of  the  pantograph 
system. 

The  fourth  slidiug  piece  (p),  being  connected  with  the  joint  A of  the  pantograph  system  by 
means  of  a separate  piece,  insures  a permanently  fixed  distance  between  (p)  and  A while  the 
instrument  is  in  use. 

The  pantograph  system  is  composed  of  six  pieces:  Tour  straight  arms,  A />,  AC , Fp,  and  F/A 
and  two  double  arms  or  levers,  CDF  and  BDG,  which  are  bent  at  right  angles  at  their  points  of 
junction  D.  The  sides  of  the  two  parallelograms  ABCD  and  DCFE  are  all  of  equal  lengths,  and 
the  six  arms  are  joined  in  A,  B , (7,  Z>,  F,  F , and  G.  The  arms  F/li  and  Fp'  are  twice  as  long  as  the 
length  of  the  side  of  the  parallelograms. 

The  pencil  which  describes  the  perspective  may  be  attached  to  the  free  end  of  either  arm 
Fp  or  TV. 

The  angles  GDB  and  EDO  being  each  equal  to  90°,  the  sum  of  the  two  other  angles  CI>B 


and  GDE  must  be  equal  to  180°,  and  as  the  sum  of  two  adjacent  angles  in  a parallelogram  is  equal 
to  180°,  it  follows  that 

(JOB  + GDE  = CDB  + DC  A 
or : 

GDE  = DC  A 


This  shows  that  the  two  parallelograms  FGDE  and  CDB  A must  be  equiangular,  and  as  their 
sides  are  equal  in  length,  the  parallelograms  themselves  must  be  equal,  and  the  diagonals  FD  and 
GE  of  the  one  are  equal  to  BC  and  AD  of  the  other,  respectively. 

The  two  long  arms  Fp'  and  Fp  being  of  equal  lengths,  pp'  will  be  parallel  to  GE , both  will 
be  perpendicular  to  the  direction  of  XY , and  pp'  will  pass  through  D.  We  have,  therefore, 
Dp'  — Dp  = GE  = DA. 

Use  of  the  perspectograph. — The  sliding  piece  s is  secured  to  the  working  board,  over  the  platted 
position  of  the  camera  station  on  the  ground  plan,  still  permitting  a gliding  movement  of  the  arm 
sM  in  the  direction  sM  (fig.  124).  The  center  line  of  RT  is  brought  into  a position  parallel  to  the 
platted  ground  line,  and  its  position  is  also  secured  to  the  board.  The  sliding  piece  (8),  finally,  is 
moved  from  s (in  the  groove  of  RT)  until  s ( S ) is  equal  to  the  elevation  of  the  station  8 above  the 
ground  plane,  also  securing  (S)  in  this  position,  when  it  will  still  permit  a gliding  movement  of  the 
arm  <S  ) 2/ in  the  direction  of  (8)  M.  The  center  line  of  the  wooden  ruler  X Y is  placed  upon  the 
ground  line  (picture  trace)  on  the  ground  plan. 

The  manipulation  of  the  instrument  and  its  general  working  will  now  readily  be  understood. 


732 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


°(a.) 


Fig  IZS 


For  instance,  when  the  tracer  M is  moved  in  a direction  parallel  to  ET  or  to  XY,  the  arm  sM  will 
move  the  slide  OD  in  the  same  direction.  The  distance  0 (pi)  remaining  unchanged — as  long  as  s (S) 
undergoes  no  change — (pi)  A will  also  remain  of  a constant  length.  Hence,  AD  and  also  GE,  as 
well  as  Dpt,  undergo  no  changes,  and  the  pencil  in  pi  or  in  pi'  will  trace  a line  parallel  to  XY, 
representing  the  perspective  of  a line  of  the  ground  plan  (the  one  traced  by  ill")  parallel  to  the 

picture  plane. 

When  If  is  moved  in  the  direction  of  sM,  away  from 
XY,  the  positions  of  0 and  D remain  the  same,  but  Opi 
will  be  lengthened,  (pi)  moves  to  the  right,  or  away  from 
0,  carrying  the  point  A with  it  ( A (pi)  being  a constant 
length)  and  increasing  the  length  of  the  diagonal  DA  in 
proportion  to  the  increase  of  the  length  of  0 (pi).  DA 
being  equal  to  GE  = Dpi  (Dpi'),  the  latter  will  also  be 
lengthened,  and  pi  will  be  moved  down,  or  away  from 
XY,  by  the  same  amount  as  (pi)  is  moved  to  the  right. 
The  relation  between  the  construction  made  in  fig.  123 
and  the  mechanical  platting  by  means  of  the  perspecto- 
graph  will  now  be  evident. 

VII.  Professor  Jlauck's  tr Holograph. — This  instru- 
ment has  been  described  by  Dr.  G.  Hauck  in  a memorial 
commemorating  the  opening  of  the  new  building  of  the  Royal  Technical  High  School  at  Charlot- 
tenburg,  near  Berlin,  November  2,  1884.  It  serves  to  reconstruct  an  object  from  two  perspectives 
of  the  same  that  had  been  obtained  from  two  different  points  of  view. 

The  principles  which  underlie  the  construction  of  this  instrument  hold  equally  good  for  the 
construction  of  an  instrument  to  be  used  for  the  mechanical  platting  of  the  ground  plan  of  any 
object  represented  on  two  photographs  obtained  from  different  stations. 

In  1887,  Prof.  F.  Schiffner  already  suggested  the  changes  to  be  made  to  Dr.  Hauck’s  instrument, 
in  order  to  render  it  available  as  an  instrument  of  precision  for  the  use  of  the  phototopographer ; 
still  it  seems  that  mechanical  diffi- 
culties in  its  manufacture  are  yet  to  jfa) 

be  overcome,  as  the  writer  has  not 
met  with  any  record  of  such  a per- 
fected instrument  having  been  either 
in  use  or  even  been  constructed. 

In  Chapter  I it  had  been  shown 
that  a point,  A,  photographed  from 
two  stations  8 and  8X,  may  be  platted 
in  horizontal  plan,  if  the  two  picture 
traces,  gg  and  gxgx,  and  the  two  cam- 
era stations,  8 and  Sx,  are  given  on 
the  horizontal  plan,  fig.  125. 

The  two  picture  planes  may  be 
revolved  about  their  ground  lines,  gg 
and  gxgx,  into  the  ground  or  platting  plane,  when  (a)  and  (ax)  will  be  the  two  images  of  the  point,  A , 
revolved  into  the  ground  plane.  If  we  draw  lines  through  (a)  and  (a x)  perpendicular  to  the  corre- 
sponding ground  lines  gg  and  gxgx,  then  a’  and  ax  will  be  the  (horizontal)  projections  of  the  picture 
points,  a and  eq,into  the  platting  plane,  and  the  intersection,  A',  of  the  radials  $«'and  /Sja/will  locate 
the  positions  on  the  platting  sheet  of  the  point  A,  pictured  on  the  two  plates  as  a and  ax , respectively. 

This  graphic  determination  of  the  platted  position  A'  of  the  point  A maybe  accomplished 
mechanically  by  placing  slotted  rulers  with  their  center  lines  upon  gg  and  gxgx,  fig.  126,  and 
indicating  the  directions  of  the  perpendiculars,  dropped  from  the  pictured  points  (revolved  into 
the  horizontal  plan)  upon  the  ground  lines,  by  two  arms  (a)  be  and  a'b  of  a pantograph 
combination,  where 

(a)b  = be  — a'b 
or 

(ax)bx  ~ bxcx  = a'xbx 


Fig.  126 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


733 


Tlie  points  (■ a)a ' and  c will  always  be  situated  on  the  periphery  of  a semicircle  described 
about  b as  the  center,  and,  as  the  points  c and  a'  are  permanently  held  on  the  line  gg,  the  angle 
(a)  a'c  (angle  of  the  periphery  subtending  the  semicircle)  will  be  equal  to  90°  for  all  inclinations  that 
may  be  given  (a)c  against  gg.  The  directions  of  the  radials  8a'  are  laid  down  mechanically  by 
means  of  two  slotted  rulers  Sa'  and  8xa'x,  held  in  position  by  the  studs  in  8 and  a'  (and  Sx  and  a'x, 
respectively),  both  rulers  being  revolvable  about  the  fixed  points  S and  8. 

This  instrument,  of  which  the  characteristic  features  are  illustrated  in  fig.  120,  performs  the 
constructions  mechanically  that  were  made  graphically  or  geometrically  in  fig.  125. 

The  slotted  rulers  gg  and  gxg\  are  secured  to  the  platting  board  (their  center  lines  on  the 
picture  traces)  by  means  of  thumb  tacks  T.  The  pantograph  arms  (a)  c — (ax)cx  — and  a'b  — ( a'x ) bx  — 
are  connected  with  these  rulers  by  means  of  sliding  joints  c (and  c, ) and  a'  (and  a'x),  while  the  studs 
which  mark  the  stations  8 and  8X  end  in  cylindrical  projections  that  fit  into  the  slots  of  the  rulers 
8a'  and  Sxa'x,  the  latter  fitting  also  over  similar  cylindrical  attachments  to  a ' and  a\,  in  such  a 
way  that  the  rulers  Sa'  and  Sxa'x  may  freely  glide  over  the  points  8 and  a'  (or  Sx  and  a'x)  and  at 
the  same  time  may  revolve  about  the  fixed  points  S and  Sx,  respectively. 

The  points  (a)  and  (ax)  are  provided  with  tracers,  and  a pencil  slide  is  attached  to  the  inter- 
section of  the  rulers  8a'  and  Sxa' i (in  A')  in  such  a way  that  the  pencil  point  may  freely  slide 
either  way  in  the  grooves  of  8a'  and  Sxa'x. 

A comparison  between  the  figures  Nos.  126  and  127  will  plainly  show  that  A'  will  always 
represent  the  platted  position  of  the  point  A,  derived  from  its  two  images  a and  (uj)  (revolved  into 
horizontal  plan).  Still,  it  may  not  always  be  possible  to  identify  both  images  of  the  same  point  on 
the  two  pictures,  and,  in  order  to  apply  Professor  Hauck’s  method  to  identify  the  second  image 
(on  the  second  photograph)  by  means  of  the  so-called  “kernelpoiuts,”  the  instrument  shown  in 
fig.  126  should  be  modified  in  such  a way  that  the  point  of  the  second  tracer  may  always  be  upon 
the  image  (on  the  second  picture)  which  corresponds  to  the  point  designated  by  the  first  tracer  on 
the  first  picture  (revolved  into  the  ground  plane). 

We  had  seen  (Chapter  I)  that  the  line  connecting  the  image  of  any  point  A on  the  first  picture 
with  the  image  of  the  second  camera  station  (with  the  kernelpoint  («i),  fig.  127) — and  the  line  — 
connecting  the  image  of  the  same  point  A on  the  second  picture  with  the  image  of  the  first  camera 
station  (with  the  kernelpoint  (s),  fig.  127) — will  bisect  the  same  point  a of  the  line  of  intersection 
of  the  two  picture  planes. 

The  picture  planes  being  vertical,  this  line  of  intersection  will  be  represented  by  the  vertical 
line  through  the  point  fi  of  the  ground  plane  (through  the  point  of  intersection  of  the  two  picture 
traces  or  ground  lines  gg  and  gxgx).  The  picture  planes  having  been  revolved  about  their  ground 
lines  as  axes  into  the  horizontal  plane,  this  line  of  intersection,  <7/1,  also  revolved  into  the  ground 
plane  (once  about  gg  and  once  about  gxgx)  will  appear  twice  in  the  platting  plane,  once  as  £2(i 7), 
perpendicular  to  gg  in  £2,  and  again  as  £2(0  x),  perpendicular  to  gxg,  in  ,Q. 

As  the  points  (a)  and  (ffx)  represent  the  same  point  <7  revolved  into  the  horizontal  plane,  once 
about  gg  and  again  about  gxgx  as  axes,  the  lengths  ( 0) £2  and  ( 0X)£2  must  be  equal. 

In  order,  therefore,  that  this  instrument,  fig.  126,  may  work  in  harmony  with  the  principles 
that  underlie  Professor  Hauck’s  method,  it  will  have  to  be  modified  to  fulfill  the  following 
conditions : 

A line  drawn  through  the  kernelpoint  Si,  fig.  127,  and  any  point  pictured  on  the  first  photograph 
and  a line  drawn  through  the  kernelpoint  s and  the  image  of  the  same  point  on  the  second  photo- 
graph are  to  intersect  the  line  of  intersection  of  both  picture  planes  in  the  same  point  a,  or  the 
two  hues  revolved  (with  the  picture  planes)  into  the  horizontal  plane  must  bisect  the  revolved 
lines  (0)£2  and  (0X)£2  (of  the  line  of  intersection  of  the  picture  planes)  in  points  (0)  and  (cq),  both 
to  be  equidistant  from  £2. 

The  complete  instrument,  in  a general  way,  is  represented  in  fig.  127.  The  two  slotted  rulers 
gg  and  gxgx  of  fig.  126  have  been  supplied  with  additional  arms  .(2(0)  and  .(2(ax),  each  arm  includ- 
ing an  angle  of  90°  with  its  ruler.  These  rectangular  elbow  pieces  are  secured  to  the  platting 
board  by  tour  thumb  tacks  T after  the  rulers  gf2  and  gx£2  had  been  placed  with  their  center  lines 
upon  the  picture  traces  gg  and  gxgx,  respectively,  in  such  a way  that  the  intersections  of  the  center 
lines  of  the  elbow  rulers  (at  the  rectangular  elbow  ends  of  the  rulers)  coincide  with  the  intersection 
£2  of  the  ground  lines  or  picture  traces  gg  and  gxgx. 


734 


UNITED  STATES  COAST  AND  GEODETIC  SURVEY. 


The  pantograph  arms,  representing  the  ground  lines  of  the  pictures,  are  attached  to  the  rulers 
the  same  as  shown  in  tig.  126.  Studs  are  inserted  into  the  kernelpoints  (Si)  and  (s),  and  the  arms 
12(c)  and  12(Ci)  support  a ruler  (c)(c1),  which  may  glide  freely  over  these  arms  of  the  elbow  pieces. 
To  cut  off  equal  lengths  by  this  ruler  (c)(C])  on  the  elbow  arms  12(c)  and  12(ct),  the  angle  d{a)e 
is  adjustable,  and  it  should  be  regulated  for  each  set  of  two  picture  traces  to  make: 

(c)12  = 

When  (c)d  is  moved  along  the  slot  of  (c)12  the  slide  point  (Ci)  will  move  along  (Cj)12,  12(c) 
always  being  equal  to  12  (Ci). 

The  screw  d serves  to  clamp  the  angle  d(ff)e  for  any  opening  corresponding  to  the  angle 

/ 


k' 


g£lg{  included  between  the  picture  traces.  Slotted  rulers  are  now  placed  over  the  studs  that 
mark  the  kernelpoints  (.sq ) and  (s),  their  slots  also  receiving  the  cylindrical  prolongations  of  the 
tracers  (a)  and  (at)  and  those  of  the  slide  points  (c)  and  (C]),  respectively.  To  complete  the 
instrument,  two  slotted  rulers  R8  and  R\8{  are  finally  placed  over  the  studs  S and  Si  (marking 
the  platted  positions  of  the  two  stations)  and  over  the  sliding  joints  a1  and  a'  (which  are  the  same 
as  those  in  iig.  126).  At  their  point  of  intersection  A'  the  sliding  pencil  point  is  inserted  (into  the 
slots  of  these  two  rulers),  which  finally  completes  this  instrument  as  illustrated  in  fig.  127. 

If  we  now  move  the  tracer  («)  on  the  first  photograph,  the  pantograph  arms  (a)  c and  ha'  will 
change  the  position  of  the  ruler  SR  (into  the  direction  of  the  radial  from  8,  to  the  horizontal 
projection,  on  the  picture  trace,  of  the  pictured  point  designated  by  the  tracer  point  (a)  on  the 
first  photograph),  and  the  ruler  (a)  (s,)  is  moved,  locating  the  point  (<r). 


REPORT  FOR  1897 PART  II.  APPENDIX  NO.  10. 


735 


This  change  in  the  position  of  (a)  produces  a corresponding  change  in  the  sliding  point  (Oi), 
which  in  turn  changes  the  position  of  the  tracer  (a{),  causing  the  pantograph  arms  {a{)  ex  and  bxa\ 
to  move,  and  a change  in  the  position  of  will  cause  the  radial  ruler  Z/j/Si  to  assume  a new  posi- 
tion also.  The  intersection  of  R8  with  the  new  position  of  RiSi  will  locate  the  platted  position  in 
horizontal  plan  of  the  point  under  the  tracer  (a)  on  the  first  photograph,  without  having  actually 
identified  the  corresponding  image  of  the  (same)  point  under  the  tracer  (%)  on  the  second  picture. 

If  a line  on  either  photograph  is  followed  out  by  one  of  the  tracers  (a)  or  (%),  the  pencil  point 
A'  will  draw  the  horizontal  projection  of  the  line  given  in  perspective  (the  second  tracer  being 
observed  chiefly  as  a check  or  to  aid  the  general  working  of  the  instrument  by  a gentle  tapping 
when  the  movements  of  the  various  parts  of  the  instrument  are  retarded  by  too  much  friction  or 
lost  motion). 

. Until  now  no  perfect  perspectograph  has  been  constructed,  and,  no  matter  how  accurately 
such  instruments,  like  the  one  just  described,  may  be  made  by  the  mechanician,  there  will  always 
remain  some  unavoidable  imperfections  in  the  material  or  in  the  workmanship  of  the  instrument 
that  will  produce  more  or  less  error  in  the  results. 

For  accurate  and  precise  work,  therefore,  the  iconometric  platting  should  be  accomplished 
with  the  aid  of  graphic  or  geometrical  constructions  for  all  the  control  work  of  the  survey,  using- 
perspective  instruments  only  for  filling  in  such  details  which,  in  an  instrumental  survey  of  a 
similar  character,  would  be  sketched  in  by  the  topographer. 


